Cartesian product of graphspath factorizationPartition of G into edge-disjoint H-factors is called H-factorization of G. Muthusamy and Paulraja have conjectured that for k ≥ 3, Km□Knhas a Pk-factorization if and only if mn ≡ 0 (modk) and k(m + n - 2) ≡ 0 (mod2(k - 1))...
graphs The Cartesian product of graphs.In graph theory,the Cartesian product G□H of graphs G and H is a graph such that •the vertex set of G□H is the Cartesian product V(G)×V(H);and •any two vertices(u,u')and(v,v')are adjacent in G□ H if and only if either •u...
Cartesianproductofgraphs TheCartesianproductofgraphs. Ingraphtheory,theCartesianproductG□Hofgraphs GandHisagraphsuchthat •thevertexsetofG□HistheCartesianproduct V(G)×V(H);and •anytwovertices(u,u')and(v,v')areadjacentinG□ Hifandonlyifeither ...
We denote the path with m vertices by Pm and the Cartesian product of graphs G and H by G × H . In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with re?ective symmetry by Pfaf?ans, Adv. Appl. Math. 32 (2004) 175...
We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one unloop
and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [19], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results: 1. Let T ...
Cartesian product of graphsLet G be a simple, finite and connected graph. An outer-connected vertex edge dominating set, abbreviated OCVEDS of G is a subset D of vertices of G such that D is a vertex edge dominating set and the graph GD is connected. The outer-connected vertex edge ...
Abstract We show that every nontrivial finite or infinite connected directed graph with loops and at least one vertex without a loop is uniquely representable as a Cartesian or weak Cartesian product of prime graphs. For finite graphs the factorization can be computed in linear time and space....
The Roman domination number gamma(R)(G), of G, is the minimum weight of a Roman dominating function on G. In this paper, we obtain that for any two graphs G and H, the k-domination number of the Cartesian product of G and H is bounded below by gamma(G)gamma(k)(H)/2. Also,...
Crossing numbers of cartesian products of stars with 5-vertex graphs 五阶图与星图的笛卡尔积交叉数 2. The relation between the Cartesian product and authentication codes is studied in this paper. 该文研究了笛卡尔积与认证码的关系,根据笛卡儿积的结构特点,提出了一种将认证符信息嵌入到编码规则的思想...