A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and d...A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.展开更多
With the advancement of Vehicle-to-Everything(V2X)technology,efficient resource allocation in dynamic vehicular networks has become a critical challenge for achieving optimal performance.Existing methods suffer from h...With the advancement of Vehicle-to-Everything(V2X)technology,efficient resource allocation in dynamic vehicular networks has become a critical challenge for achieving optimal performance.Existing methods suffer from high computational complexity and decision latency under high-density traffic and heterogeneous network conditions.To address these challenges,this study presents an innovative framework that combines Graph Neural Networks(GNNs)with a Double Deep Q-Network(DDQN),utilizing dynamic graph structures and reinforcement learning.An adaptive neighbor sampling mechanism is introduced to dynamically select the most relevant neighbors based on interference levels and network topology,thereby improving decision accuracy and efficiency.Meanwhile,the framework models communication links as nodes and interference relationships as edges,effectively capturing the direct impact of interference on resource allocation while reducing computational complexity and preserving critical interaction information.Employing an aggregation mechanism based on the Graph Attention Network(GAT),it dynamically adjusts the neighbor sampling scope and performs attention-weighted aggregation based on node importance,ensuring more efficient and adaptive resource management.This design ensures reliable Vehicle-to-Vehicle(V2V)communication while maintaining high Vehicle-to-Infrastructure(V2I)throughput.The framework retains the global feature learning capabilities of GNNs and supports distributed network deployment,allowing vehicles to extract low-dimensional graph embeddings from local observations for real-time resource decisions.Experimental results demonstrate that the proposed method significantly reduces computational overhead,mitigates latency,and improves resource utilization efficiency in vehicular networks under complex traffic scenarios.This research not only provides a novel solution to resource allocation challenges in V2X networks but also advances the application of DDQN in intelligent transportation systems,offering substantial theoretical significance and practical value.展开更多
Dialogue State Tracking(DST)is a critical component of task-oriented spoken dialogue systems(SDS),tasked with maintaining an accurate representation of the conversational state by predicting slots and their correspond...Dialogue State Tracking(DST)is a critical component of task-oriented spoken dialogue systems(SDS),tasked with maintaining an accurate representation of the conversational state by predicting slots and their corresponding values.Recent advances leverage Large Language Models(LLMs)with prompt-based tuning to improve tracking accuracy and efficiency.However,these approaches often incur substantial computational and memory overheads and typically address slot extraction implicitly within prompts,without explicitly modeling the complex dependencies between slots and values.In this work,we propose PUGG,a novel DST framework that constructs schema-driven prompts to fine-tune GPT-2 and utilizes its tokenizer to implement a memory encoder.PUGG explicitly extracts slot values via GPT-2 and employs Graph Attention Networks(GATs)to model and reason over the intricate relationships between slots and their associated values.We evaluate PUGG on four publicly available datasets,where it achieves stateof-the-art performance across multiple evaluation metrics,highlighting its robustness and generalizability in diverse conversational scenarios.Our results indicate that the integration of GPT-2 substantially reduces model complexity and memory consumption by streamlining key processes.Moreover,prompt tuning enhances the model’s flexibility and precision in extracting relevant slot-value pairs,while the incorporation of GATs facilitates effective relational reasoning,leading to improved dialogue state representations.展开更多
High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface compl...High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface complexity and tendency for elemental segregation,which results in discrepancies between bulk and surface compositions,pose challenges for direct investigation via density functional theory.To address this,Monte Carlo simulations combined with molecular dynamics were employed to model surface segregation across a broad range of elements,including Cu,Ag,Au,Pt,Pd,and Al.The analysis revealed a trend in surface segregation propensity following the order Ag>Au>Al>Cu>Pd>Pt.To capture the correlation between surface site characteristics and the free energy of multi-dentate CO_(2)reduction intermediates,a graph neural network was designed,where adsorbates were transformed into pseudo-atoms at their centers of mass.This model achieved mean absolute errors of 0.08–0.15 eV for the free energies of C_(2)intermediates,enabling precise site activity quantification.Results indicated that increasing the concentration of Cu,Ag,and Al significantly boosts activity for CO and C_(2)formation,whereas Au,Pd,and Pt exhibit negative effects.By screening stable composition space,promising HEA bulk compositions for CO,HCOOH,and C_(2)products were predicted,offering superior catalytic activity compared to pure Cu catalysts.展开更多
Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph...Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.展开更多
A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vert...A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.展开更多
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic the...A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs.展开更多
For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which ...For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.展开更多
In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission...In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means.展开更多
The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the ...The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.展开更多
Let Kn be a complete graph on n vertices. In this paper, we find the necessary conditions for the existence of a 6-cycle system of Kn - L for every nearly 2-regular leave L of Kn. This condition is also sufficient whe...Let Kn be a complete graph on n vertices. In this paper, we find the necessary conditions for the existence of a 6-cycle system of Kn - L for every nearly 2-regular leave L of Kn. This condition is also sufficient when the number of vertices of L is n - 4.展开更多
A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can e...A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.展开更多
The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method,...The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method, we provide an O（m） time algorithm to solve the 2-step domination problem on block graphs, a superclass of trees.展开更多
It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of ev...It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.展开更多
A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set ...A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].展开更多
Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological in...Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.展开更多
文摘A vertex labeling f ： V →Z2 of a simple graph G = （V, E） induces two edge labelings The friendly index set and the product-cordial index set of G are defined as the setsf is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.
基金Project ZR2023MF111 supported by Shandong Provincial Natural Science Foundation。
文摘With the advancement of Vehicle-to-Everything(V2X)technology,efficient resource allocation in dynamic vehicular networks has become a critical challenge for achieving optimal performance.Existing methods suffer from high computational complexity and decision latency under high-density traffic and heterogeneous network conditions.To address these challenges,this study presents an innovative framework that combines Graph Neural Networks(GNNs)with a Double Deep Q-Network(DDQN),utilizing dynamic graph structures and reinforcement learning.An adaptive neighbor sampling mechanism is introduced to dynamically select the most relevant neighbors based on interference levels and network topology,thereby improving decision accuracy and efficiency.Meanwhile,the framework models communication links as nodes and interference relationships as edges,effectively capturing the direct impact of interference on resource allocation while reducing computational complexity and preserving critical interaction information.Employing an aggregation mechanism based on the Graph Attention Network(GAT),it dynamically adjusts the neighbor sampling scope and performs attention-weighted aggregation based on node importance,ensuring more efficient and adaptive resource management.This design ensures reliable Vehicle-to-Vehicle(V2V)communication while maintaining high Vehicle-to-Infrastructure(V2I)throughput.The framework retains the global feature learning capabilities of GNNs and supports distributed network deployment,allowing vehicles to extract low-dimensional graph embeddings from local observations for real-time resource decisions.Experimental results demonstrate that the proposed method significantly reduces computational overhead,mitigates latency,and improves resource utilization efficiency in vehicular networks under complex traffic scenarios.This research not only provides a novel solution to resource allocation challenges in V2X networks but also advances the application of DDQN in intelligent transportation systems,offering substantial theoretical significance and practical value.
基金supported by the MSIT(Ministry of Science and ICT),Republic of Korea,under the ITRC(Information Technology Research Centre)support program(IITP-2024-RS-2024-00437191)supervised by the IITP(Institute for Information&Communications Technology Planning&Evaluation).
文摘Dialogue State Tracking(DST)is a critical component of task-oriented spoken dialogue systems(SDS),tasked with maintaining an accurate representation of the conversational state by predicting slots and their corresponding values.Recent advances leverage Large Language Models(LLMs)with prompt-based tuning to improve tracking accuracy and efficiency.However,these approaches often incur substantial computational and memory overheads and typically address slot extraction implicitly within prompts,without explicitly modeling the complex dependencies between slots and values.In this work,we propose PUGG,a novel DST framework that constructs schema-driven prompts to fine-tune GPT-2 and utilizes its tokenizer to implement a memory encoder.PUGG explicitly extracts slot values via GPT-2 and employs Graph Attention Networks(GATs)to model and reason over the intricate relationships between slots and their associated values.We evaluate PUGG on four publicly available datasets,where it achieves stateof-the-art performance across multiple evaluation metrics,highlighting its robustness and generalizability in diverse conversational scenarios.Our results indicate that the integration of GPT-2 substantially reduces model complexity and memory consumption by streamlining key processes.Moreover,prompt tuning enhances the model’s flexibility and precision in extracting relevant slot-value pairs,while the incorporation of GATs facilitates effective relational reasoning,leading to improved dialogue state representations.
文摘High-entropy alloy(HEA)offer tunable composition and surface structures,enabling the creation of novel active sites that enhance catalytic performance in renewable energy application.However,the inherent surface complexity and tendency for elemental segregation,which results in discrepancies between bulk and surface compositions,pose challenges for direct investigation via density functional theory.To address this,Monte Carlo simulations combined with molecular dynamics were employed to model surface segregation across a broad range of elements,including Cu,Ag,Au,Pt,Pd,and Al.The analysis revealed a trend in surface segregation propensity following the order Ag>Au>Al>Cu>Pd>Pt.To capture the correlation between surface site characteristics and the free energy of multi-dentate CO_(2)reduction intermediates,a graph neural network was designed,where adsorbates were transformed into pseudo-atoms at their centers of mass.This model achieved mean absolute errors of 0.08–0.15 eV for the free energies of C_(2)intermediates,enabling precise site activity quantification.Results indicated that increasing the concentration of Cu,Ag,and Al significantly boosts activity for CO and C_(2)formation,whereas Au,Pd,and Pt exhibit negative effects.By screening stable composition space,promising HEA bulk compositions for CO,HCOOH,and C_(2)products were predicted,offering superior catalytic activity compared to pure Cu catalysts.
文摘Diab proved the following graphs are Cordial;Pm K1,n if and only if(m,n) =(1,2);Cm K1,n;Pm Kn;Cm Kn for all m and n except m ≡ 2(mod 4).In this paper,we proved the Cordiality on the union of 3-regular connected graph K3 and cycle Cm.First we have the Lemma 2,if uv ∈ E(G),G is Cordial,we add 4 vertices x,y,z,w in sequence to the edge uv,obtain a new graph denoted by G*,then G* is still Cordial,by this lemma,we consider four cases on the union of 3-regular connected graph R3,and for every case we distinguish four subcases on the cycle Cm.
文摘A subset of the vertex set of a graph is a feedback vertex set of the graph if the resulting graph is a forest after removed the vertex subset from the graph. A polynomial algorithm for finding a minimum feedback vertex set of a 3-regular simple graph is provided.
基金Supported by the National Natural Science Foundation of China (10671081)
文摘A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph.In this paper,we show some necessary conditions that a 2-walk（a,b）-linear graph must obey.Using these conditions and some basic theorems in graph theory,we characterize all 2-walk linear graphs with small cyclic graphs without pendants.The results are given in sort on unicyclic,bicyclic,tricyclic graphs.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1097102510901035)
文摘For a graph G and two positive integers j and k, an m-L（j, k）-edge-labeling of G is an assignment on the edges to the set {0,..., m}, such that adjacent edges receive labels differing by at least j, and edges which are distance two apart receive labels differing by at least k. The λ′j,k-number of G is the minimum m of an m-L（j, k）-edge-labeling admitted by G.In this article, we study the L（1, 2）-edge-labeling for paths, cycles, complete graphs, complete multipartite graphs, infinite ？-regular trees and wheels.
基金supported in part by the National Natural Science Foundation of China(61901231)in part by the National Natural Science Foundation of China(61971238)+3 种基金in part by the Natural Science Foundation of Jiangsu Province of China(BK20180757)in part by the open project of the Key Laboratory of Dynamic Cognitive System of Electromagnetic Spectrum Space,Ministry of Industry and Information Technology(KF20202102)in part by the China Postdoctoral Science Foundation under Grant(2020M671480)in part by the Jiangsu Planned Projects for Postdoctoral Research Funds(2020z295).
文摘In this paper,we jointly design the power control and position dispatch for Multi-Unmanned Aerial Vehicle(UAV)-enabled communication in Device-to-Device(D2D)networks.Our objective is to maximize the total transmission rate of Downlink Users(DUs).Meanwhile,the Quality of Service(QoS)of all D2D users must be satisfied.We comprehensively considered the interference among D2D communications and downlink transmissions.The original problem is strongly non-convex,which requires high computational complexity for traditional optimization methods.And to make matters worse,the results are not necessarily globally optimal.In this paper,we propose a novel Graph Neural Networks(GNN)based approach that can map the considered system into a specific graph structure and achieve the optimal solution in a low complexity manner.Particularly,we first construct a GNN-based model for the proposed network,in which the transmission links and interference links are formulated as vertexes and edges,respectively.Then,by taking the channel state information and the coordinates of ground users as the inputs,as well as the location of UAVs and the transmission power of all transmitters as outputs,we obtain the mapping from inputs to outputs through training the parameters of GNN.Simulation results verified that the way to maximize the total transmission rate of DUs can be extracted effectively via the training on samples.Moreover,it also shows that the performance of proposed GNN-based method is better than that of traditional means.
文摘The number of rooted nearly 2-regular maps with the valency of root-vertex, the number of non-rooted vertices and the valency of root-face as three parameters is obtained. Furthermore, the explicit expressions of the special cases including loopless nearly 2-regular maps and simple nearly 2-regular maps in terms of the above three parameters are derived.
基金Supported by the National Natural Science Foundation of China (Grant No.11071163)
文摘Let Kn be a complete graph on n vertices. In this paper, we find the necessary conditions for the existence of a 6-cycle system of Kn - L for every nearly 2-regular leave L of Kn. This condition is also sufficient when the number of vertices of L is n - 4.
基金Supported by the National Natural Science Foundation of China(11171129)
文摘A graph has exactly two main eigenvalues if and only if it is a 2-walk linear graph. In this paper, we show some structural properties that a 2-walk （a, b）-linear graph holds. According to these properties, we can estimate and characterize more 2-walk linear graphs that have exactly two main eigenvalues.
基金Supported by the National Natural Science Foundation of China(Grant No.11271365)the Domestic Senior Visiting Scholar Program in Higher Occupation Colleges in Jiangsu Province(Grant No.2014FX075)
文摘The 2-step domination problem is to find a minimum vertex set D of a graph such that every vertex of the graph is either in D or at distance two from some vertex of D. In the present paper, by using a labeling method, we provide an O（m） time algorithm to solve the 2-step domination problem on block graphs, a superclass of trees.
基金Supported by National Natural Science Foundation of China(Grant No.12071442)the Fundamental Research Funds for the Central Universities under(Grant No.020314380035)。
文摘It is well-known that the Petersen graph is nonhamiltonian.A very short proof for this result was presented in[2]due to D.B.West.In this note,by extending the proof technique in[2],we briefly show that the girth of every 3-regular hamiltonian graph on n≥10 vertices is at most(n+4)/3.
文摘A set D of vertices of a graph G = (V, E) is called k-dominating if every vertex v ∈V-D is adjacent to some k vertices of D. The k-domination number of a graph G, γk (G), is the order of a smallest k-dominating set of G. In this paper we calculate the k-domination number (for k = 2) of the product of two paths Pm × Pn for m = 1, 2, 3, 4, 5 and arbitrary n. These results were shown an error in the paper [1].
文摘Let G = (V;E) be a simple connected graph. The Wiener index is the sum of distances between all pairs of vertices of a connected graph. The Schultz topological index is equal to and the Modified Schultz topological index is . In this paper, the Schultz, Modified Schultz polynomials and their topological indices of Jahangir graphs J<sub>2,m</sub> for all integer number m ≥ 3 are calculated.
