Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propos...Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.展开更多
Given a digraph D =（V, A）, the competition graph G of D, denoted by C（D）, has the same set of vertices as D and an edge between vertices x and y if and only if N;（x）∩N;（y）≠Ф. In this paper, we investigate t...Given a digraph D =（V, A）, the competition graph G of D, denoted by C（D）, has the same set of vertices as D and an edge between vertices x and y if and only if N;（x）∩N;（y）≠Ф. In this paper, we investigate the competition graphs of round digraphs and give a necessary and sufficient condition for these graphs to be hamiltonian.展开更多
As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,...As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.展开更多
Let D be a digraph.The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D.The phyloge...Let D be a digraph.The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D.The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices.The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph.In this paper,we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k.We get similar results for hypergraphs.展开更多
文摘Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.
基金Supported by NSFC(11401353)TYAL of ShanxiNatural Science Foundation of Shanxi Province(2016011005)
文摘Given a digraph D =（V, A）, the competition graph G of D, denoted by C（D）, has the same set of vertices as D and an edge between vertices x and y if and only if N;（x）∩N;（y）≠Ф. In this paper, we investigate the competition graphs of round digraphs and give a necessary and sufficient condition for these graphs to be hamiltonian.
基金Shanxi Scholarship Council of China(No.2012-070)Foundation of North University of China(No.2013-12-1)
文摘As a generalization of the scrambling index and the exponent,m-competition index has been widely applied to stochastic matrices,food webs and memoryless communication systems in recent years. For a positive integer m,where 1 ≤ m ≤ n,the mcompetition index( generalized competition index) of a primitive digraph D of order n is the smallest positive integer k such that for every pair of vertices x and y,there exist m distinct vertices v_1,v_2,…,v_m such that there exist walks of length k from x to v_i and from y to v_i for 1 ≤ i ≤ m. By analyzing the structure of θ-graphs( theta graphs) and using enumeration investigation methods,the mcompetition indices of primitive θ-graphs are studied and an upper bound is provided. Moreover, some corresponding extremal θ-graphs are characterized.
文摘Let D be a digraph.The competition graph of D is the graph having the same vertex set with D and having an edge joining two different vertices if and only if they have at least one common out-neighbor in D.The phylogeny graph of D is the competition graph of the digraph constructed from D by adding loops at all vertices.The competition/phylogeny number of a graph is the least number of vertices to be added to make the graph a competition/phylogeny graph of an acyclic digraph.In this paper,we show that for any integer k there is a connected graph such that its phylogeny number minus its competition number is greater than k.We get similar results for hypergraphs.
