The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph.The kth power G^(k) of a graph G is the graph on V(G)and two vertices are adjacent if and only if their dista...The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph.The kth power G^(k) of a graph G is the graph on V(G)and two vertices are adjacent if and only if their distance in G is less or equal to k.In this paper,we computed the Wiener index of the kth power of paths and cycles for any k≥2.展开更多
Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty ve...Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 （respectively, 2n - 2fv - 2） can be embedded on Qn,k with fv ＋ f≤ n- 1 when dQn,k （u, v） is odd （respectively, dQ,~,k （u, v） is even）. Secondly, an Q,,k is （n - 2） edgefault-free hyper Hamiltonianaceable when n （ 3） and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv＋f≤2n-4.展开更多
For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [...For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [ci - cj] ≤1 for any two colors i and j, then c is an equitable edge coloring of G. The coloring c is an equitable adjacent strong edge coloring of G if it is both adjacent strong edge coloring and equitable edge coloring. The least number of colors of such a coloring c is called the equitable adjacent strong chromatic index of G. In this paper, we determine the equitable adjacent strong chromatic index of the joins of paths and cycles. Precisely, we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.展开更多
Under many aspects Italy would be ideal for cycling:the weather is favourable for a good part of the year and many historic centres are characterized by roads which would mainly be suitable for bicycle traffic.The pos...Under many aspects Italy would be ideal for cycling:the weather is favourable for a good part of the year and many historic centres are characterized by roads which would mainly be suitable for bicycle traffic.The positive aspects relating to cycling are well known,but unfortunately,the use of bicycles in Italy is still poor and the main cause of this phenomenon is certainly relating to a general lack of safety in cycling.In the last decade,in Italy the trend of road accidents and victims is generally decreasing,but,at the same time,the number of cyclists involved in road accidents increased by 24,5%,therefore,more attention to cyclists as Vulnerable Road Users is absolutely needed.The causes of this high accident rate is mainly relating to a lack of national legislation or to standards which are old,often overlapped to regional guidelines,uneven,confusing and in some case also contradictory.In terms of cycle network planning,it should be reminded that in Italy there is no regulation that establishes the criteria for a functional classification of bicycle paths.As a consequence,the infrastructure geometry and facilities(bicycle parking,places of refreshments,cycle repair shops,etc.)are not properly put in relation to the role played by the cycle path in the territory.In the course of time,we assisted to the realization of isolated cycle path trunks,generally out of a planning strategy and characterized by their own geometry.Therefore,taking also inspiration by the standards developed in other European Countries,this research tries to provide guidelines for pre-normative functional classification of cycle paths,for their design and planning,in order to obtain safe and homogeneous cycling routes in Italy.It should be noted that the technical solutions,devices and traffic regulations,adopted in other countries,are very effective for a safe cycle mobility,but need to be revised in relation to the existing Italian law.展开更多
A labeled graph is an ordered pair （G, L） consisting of a graph G and its labeling L ： V（G） → {1,2 ,n}, where n = ｜V（G）｜. An increasing nonconsecutive path in a labeled graph （G,L） is either a path （u1,u2...A labeled graph is an ordered pair （G, L） consisting of a graph G and its labeling L ： V（G） → {1,2 ,n}, where n = ｜V（G）｜. An increasing nonconsecutive path in a labeled graph （G,L） is either a path （u1,u2 uk） （k ≥ 2） in G such that L（u,） ＋ 2 ≤ L（ui＋1） for all i = 1, 2, ..., k- 1 or a path of order 1. The total number of increasing nonconsecutive paths in （G, L） is denoted by d（G, L）. A labeling L is optimal if the labeling L produces the largest d（G, L）. In this paper, a method simpler than that in Zverovich （2004） to obtain the optimal labeling of path is given. The optimal labeling of other special graphs such as cycles and stars is obtained.展开更多
A graph is called claw-free if it does not contain a claw as its induced subgraph.In this paper, we prove the following results:1)If G is a 2-connected claw-free graph on n vertices,then for any vertex v and any two d...A graph is called claw-free if it does not contain a claw as its induced subgraph.In this paper, we prove the following results:1)If G is a 2-connected claw-free graph on n vertices,then for any vertex v and any two distinct vertices x and y in V(G)-{v},G has a path containing v and all neighbors of v and connecting x and y;2) Let C be the longest cycle in a 3-connected claw-free graph G and H a component of G-C,and if H is connected but not 2-connected,then there exist nonadjacent vertices u and v in H such that |V(C)|≥(3(d(u)+)d(v))-2.展开更多
If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-k...If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-kernels and for the number of minimal quasi-kernels of oriented paths and cycles.展开更多
Sensor nodes are easily compromised to malicious attackers due to an open environment. A false injected attack which takes place on application layer is elected by the compromised node. If the false report arrives in ...Sensor nodes are easily compromised to malicious attackers due to an open environment. A false injected attack which takes place on application layer is elected by the compromised node. If the false report arrives in a base station, a false alarm is occurred, and the energy of the nodes is consumed. To detect the false report, statistical en-route filtering method is proposed. In this paper, we proposed the secure path cycle selection method using fuzzy rule-based system to consume effective energy. The method makes balanced energy consumption of each node. Moreover, the lifetime of the whole network will be increased. The base station determines the path cycle using the fuzzy rule-based system. The performance of the proposed method is demonstrated using simulation studies with the three methods.展开更多
In response to the Beautiful China development strategy,in accordance with the"applicable,economical,green and beautiful"architectural policy of the new era,green buildings have been continuously optimized a...In response to the Beautiful China development strategy,in accordance with the"applicable,economical,green and beautiful"architectural policy of the new era,green buildings have been continuously optimized and popularized.Based on the life cycle theory,from the multi-dimensional perspectives of policy,building materials,construction,design,evaluation standards,operation,etc.,this paper studied the implementation path and development trend of green buildings.It discussed the main implementation paths and restrictive factors of green buildings,and provided solutions and development directions.It mainly elaborated the influencing factors and development direction of green buildings,in order to provide a documentary support for the development of green building industry,and provide a certain reference for the ecological civilization construction of beautiful China.展开更多
Analyses of cloud water path （CWP） data over China available from the International Satellite Cloud Climatology Project （ISCCP） are performed for the period 1984-2004. Combined with GPCP precipitation data, cloud ...Analyses of cloud water path （CWP） data over China available from the International Satellite Cloud Climatology Project （ISCCP） are performed for the period 1984-2004. Combined with GPCP precipitation data, cloud water cycle index （CWCI） is also calculated. The climatic distributions of CWP are found to be dependent on large-scale circulation, topographical features, water vapor transport and similar distribution features which are found in CWCI except in the Sichuan Basin. Influenced by the Asia monsoon, CWP over China exhibits very large seasonal variations in different regions. The seasonal cycles of CWCI in different regions are consistent and the largest CWCI occurs in July. The long-term trends of CWP and CWCI are investigated, too. Increasing trends of CWP are found during the period with the largest increase found in winter. The decreasing trends of CWCI dominate most regions of China. The differences in long-term trends between CWP and CWCI suggest that CWP only can influence the variation of CWCI to a certain extent and that other factors need to be involved in cloud water cycle researches. This phenomenon reveals the complexity of the hydrological cycle related to cloud water.展开更多
Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1....Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1.85 mm. The calculated energy input based on the FSW parameters studied shows that the ultimate tensile strength （UTS） of the butt joint is obtained within a certain range of energy input of 297 kJ to 354 kJ out of total range of energy input studied from 196 kJ to 405 kJ. The fatigue behaviors of high-strength and low-strength joints performed at different stress ratios, i.e., 0.5, 0.3, 0.1, -0.3, -0.5, indicate that the fatigue behaviors of both the welds are sensitive to the microstructural features, such as stir zone （SZ）, thermo mechanically affected zone （TMAZ） and heat affected zone （HAZ）. The observed fatigue strengths were discussed in terms of the microstructure, crack path behavior and fracture surface.展开更多
Given a graph H and an integer p≥2,the edge blow-up graph H^(p+1)of H is the graph obtained by replacing each edge in H with a clique of order p+1,where the new vertices of the cliques are all distinct.The generalize...Given a graph H and an integer p≥2,the edge blow-up graph H^(p+1)of H is the graph obtained by replacing each edge in H with a clique of order p+1,where the new vertices of the cliques are all distinct.The generalized Turán number ex(n,K_(m),F)denote the maximum number of copies of K_(m)in an n-vertex F-free graph.Let C_(t)and P_(t)denote the cycle and path with t vertices,respectively.In this paper,we obtain the generalized Turán numbers ex(n,K_(m),P_(t)^(p+1)),ex(n,K_(m),C_(t)^(p+1))and characterize the unique graph for P p+1t and C p+1t respectively,when t≥3,p≥m≥3 and n is sufficiently large.展开更多
In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the ad...In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.展开更多
Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing probl...Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.12201471)the Special Foundation in Key Fields for Universities of Guangdong Province(Grant No.2022ZDZX1034).
文摘The Wiener index of a graph is defined to be the sum of the distances of all pairs of vertices in the graph.The kth power G^(k) of a graph G is the graph on V(G)and two vertices are adjacent if and only if their distance in G is less or equal to k.In this paper,we computed the Wiener index of the kth power of paths and cycles for any k≥2.
基金supported by NSFC (11071096, 11171129)NSF of Hubei Province, China (T201103)
文摘Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 （respectively, 2n - 2fv - 2） can be embedded on Qn,k with fv ＋ f≤ n- 1 when dQn,k （u, v） is odd （respectively, dQ,~,k （u, v） is even）. Secondly, an Q,,k is （n - 2） edgefault-free hyper Hamiltonianaceable when n （ 3） and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv＋f≤2n-4.
基金Supported by the Fundamental Research Funds for the Central Universities(Grant Nos. 2011B019)the National Natural Science Foundation of China (Grant Nos. 10971144+2 种基金1110102011171026)the Natural Science Foundation of Beijing (Grant No. 1102015)
文摘For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [ci - cj] ≤1 for any two colors i and j, then c is an equitable edge coloring of G. The coloring c is an equitable adjacent strong edge coloring of G if it is both adjacent strong edge coloring and equitable edge coloring. The least number of colors of such a coloring c is called the equitable adjacent strong chromatic index of G. In this paper, we determine the equitable adjacent strong chromatic index of the joins of paths and cycles. Precisely, we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.
文摘Under many aspects Italy would be ideal for cycling:the weather is favourable for a good part of the year and many historic centres are characterized by roads which would mainly be suitable for bicycle traffic.The positive aspects relating to cycling are well known,but unfortunately,the use of bicycles in Italy is still poor and the main cause of this phenomenon is certainly relating to a general lack of safety in cycling.In the last decade,in Italy the trend of road accidents and victims is generally decreasing,but,at the same time,the number of cyclists involved in road accidents increased by 24,5%,therefore,more attention to cyclists as Vulnerable Road Users is absolutely needed.The causes of this high accident rate is mainly relating to a lack of national legislation or to standards which are old,often overlapped to regional guidelines,uneven,confusing and in some case also contradictory.In terms of cycle network planning,it should be reminded that in Italy there is no regulation that establishes the criteria for a functional classification of bicycle paths.As a consequence,the infrastructure geometry and facilities(bicycle parking,places of refreshments,cycle repair shops,etc.)are not properly put in relation to the role played by the cycle path in the territory.In the course of time,we assisted to the realization of isolated cycle path trunks,generally out of a planning strategy and characterized by their own geometry.Therefore,taking also inspiration by the standards developed in other European Countries,this research tries to provide guidelines for pre-normative functional classification of cycle paths,for their design and planning,in order to obtain safe and homogeneous cycling routes in Italy.It should be noted that the technical solutions,devices and traffic regulations,adopted in other countries,are very effective for a safe cycle mobility,but need to be revised in relation to the existing Italian law.
基金Supported in part by the NNSF of China(10301010,60673048)Science and Technology Commission of Shanghai Municipality(04JC14031).
文摘A labeled graph is an ordered pair （G, L） consisting of a graph G and its labeling L ： V（G） → {1,2 ,n}, where n = ｜V（G）｜. An increasing nonconsecutive path in a labeled graph （G,L） is either a path （u1,u2 uk） （k ≥ 2） in G such that L（u,） ＋ 2 ≤ L（ui＋1） for all i = 1, 2, ..., k- 1 or a path of order 1. The total number of increasing nonconsecutive paths in （G, L） is denoted by d（G, L）. A labeling L is optimal if the labeling L produces the largest d（G, L）. In this paper, a method simpler than that in Zverovich （2004） to obtain the optimal labeling of path is given. The optimal labeling of other special graphs such as cycles and stars is obtained.
文摘A graph is called claw-free if it does not contain a claw as its induced subgraph.In this paper, we prove the following results:1)If G is a 2-connected claw-free graph on n vertices,then for any vertex v and any two distinct vertices x and y in V(G)-{v},G has a path containing v and all neighbors of v and connecting x and y;2) Let C be the longest cycle in a 3-connected claw-free graph G and H a component of G-C,and if H is connected but not 2-connected,then there exist nonadjacent vertices u and v in H such that |V(C)|≥(3(d(u)+)d(v))-2.
文摘If D is a digraph, then K∈V(D) is a quasi-kernel of D if D[K]is discrete and for each y∈V(D)-K there is x∈K such that the directed distance from y to x is less than three. We give formulae for the number of quasi-kernels and for the number of minimal quasi-kernels of oriented paths and cycles.
文摘Sensor nodes are easily compromised to malicious attackers due to an open environment. A false injected attack which takes place on application layer is elected by the compromised node. If the false report arrives in a base station, a false alarm is occurred, and the energy of the nodes is consumed. To detect the false report, statistical en-route filtering method is proposed. In this paper, we proposed the secure path cycle selection method using fuzzy rule-based system to consume effective energy. The method makes balanced energy consumption of each node. Moreover, the lifetime of the whole network will be increased. The base station determines the path cycle using the fuzzy rule-based system. The performance of the proposed method is demonstrated using simulation studies with the three methods.
文摘In response to the Beautiful China development strategy,in accordance with the"applicable,economical,green and beautiful"architectural policy of the new era,green buildings have been continuously optimized and popularized.Based on the life cycle theory,from the multi-dimensional perspectives of policy,building materials,construction,design,evaluation standards,operation,etc.,this paper studied the implementation path and development trend of green buildings.It discussed the main implementation paths and restrictive factors of green buildings,and provided solutions and development directions.It mainly elaborated the influencing factors and development direction of green buildings,in order to provide a documentary support for the development of green building industry,and provide a certain reference for the ecological civilization construction of beautiful China.
基金CAS/SAFEA International Partnership Program for Creative Research Teams, the Knowledge Innovation Program of Chinese Academy of Sciences （Project No. KZCX2-YW-202） National Basic Research Program of China （Grant No. 2006CB403600） +1 种基金 the National Natural Science Foundation of China（Grant Nos. 40437017, 40221503） ＂The Climate System Model Development and Application Studies＂ of International Partnership Creative Group program of Chinese Academy of Sciences, and the Key Sci. ＆ Tech. Supporting Project of the Ministry of Science and Technology of China（2006BAC12B03）.
文摘Analyses of cloud water path （CWP） data over China available from the International Satellite Cloud Climatology Project （ISCCP） are performed for the period 1984-2004. Combined with GPCP precipitation data, cloud water cycle index （CWCI） is also calculated. The climatic distributions of CWP are found to be dependent on large-scale circulation, topographical features, water vapor transport and similar distribution features which are found in CWCI except in the Sichuan Basin. Influenced by the Asia monsoon, CWP over China exhibits very large seasonal variations in different regions. The seasonal cycles of CWCI in different regions are consistent and the largest CWCI occurs in July. The long-term trends of CWP and CWCI are investigated, too. Increasing trends of CWP are found during the period with the largest increase found in winter. The decreasing trends of CWCI dominate most regions of China. The differences in long-term trends between CWP and CWCI suggest that CWP only can influence the variation of CWCI to a certain extent and that other factors need to be involved in cloud water cycle researches. This phenomenon reveals the complexity of the hydrological cycle related to cloud water.
文摘Friction stir welding （FSW） of 6061 aluminium alloy butt joint was carried out at each rotation speed of 600, 800, 1000, 1200 r/min for two different travel speeds, 80 and 100 mm/min, at a constant probe depth of 1.85 mm. The calculated energy input based on the FSW parameters studied shows that the ultimate tensile strength （UTS） of the butt joint is obtained within a certain range of energy input of 297 kJ to 354 kJ out of total range of energy input studied from 196 kJ to 405 kJ. The fatigue behaviors of high-strength and low-strength joints performed at different stress ratios, i.e., 0.5, 0.3, 0.1, -0.3, -0.5, indicate that the fatigue behaviors of both the welds are sensitive to the microstructural features, such as stir zone （SZ）, thermo mechanically affected zone （TMAZ） and heat affected zone （HAZ）. The observed fatigue strengths were discussed in terms of the microstructure, crack path behavior and fracture surface.
基金Supported by the National Nature Science Foundation of China(Grant Nos.12571375,12331012)。
文摘Given a graph H and an integer p≥2,the edge blow-up graph H^(p+1)of H is the graph obtained by replacing each edge in H with a clique of order p+1,where the new vertices of the cliques are all distinct.The generalized Turán number ex(n,K_(m),F)denote the maximum number of copies of K_(m)in an n-vertex F-free graph.Let C_(t)and P_(t)denote the cycle and path with t vertices,respectively.In this paper,we obtain the generalized Turán numbers ex(n,K_(m),P_(t)^(p+1)),ex(n,K_(m),C_(t)^(p+1))and characterize the unique graph for P p+1t and C p+1t respectively,when t≥3,p≥m≥3 and n is sufficiently large.
文摘In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.
文摘Let be an undirected graph. The maximum cycle packing problem in G then is to find a collection of edge-disjoint cycles C<sub>i</sup>in G such that s is maximum. In general, the maximum cycle packing problem is NP-hard. In this paper, it is shown for even graphs that if such a collection satisfies the condition that it minimizes the quantityon the set of all edge-disjoint cycle collections, then it is a maximum cycle packing. The paper shows that the determination of such a packing can be solved by a dynamic programming approach. For its solution, an-shortest path procedure on an appropriate acyclic networkis presented. It uses a particular monotonous node potential.
