WebApr 27, 2024 · Definitions. A directed graph is called strongly connected if there is a path in each direction between each pair of vertices of the graph. That is, a path exists from the … WebAug 1, 1996 · Abstract. There are four standard products of graphs: the direct product, the Cartesian product, the strong product and the lexicographic product. The chromatic …
Main results - STRONG RESOLVABILITY IN PRODUCT GRAPHS
WebJan 1, 2024 · The Wiener index of a connected graph G is the sum of distances between all pairs of vertices of G. The strong product is one of the four most investigated graph products. In this paper the ... WebAug 9, 2024 · Graph product plays a key role in many applications of graph theory because many large graphs can be constructed from small graphs by using graph products. Here, we discuss two of the most frequent graph-theoretical products. ... Resistance Distance in Tensor and Strong Product of Path or Cycle Graphs Based … boc hk esg
Wiener index of strong product of graphs - Semantic Scholar
WebThis note shows that for two connected graphs G1 and G2 the edge-connectivity λ(G1£G2) equals min, and fully describes the structure of possible minimum edge cut sets in strong products of graphs. The strong product G1 £G2 of graphs G1 and G2 is the graph with V (G1) × V (G2) as the vertex set, and two distinct vertices (x1, x2) and (y1, y2) are … Webout for products of directed graphs by McAndrew (5) and Harary and Trauth (2). In the present paper, we are concerned with the connectedness of products of arbitrary families of graphs, and the question, first considered in (1, p. 152), of the uniqueness of the decomposition of a graph into indecomposable factors. We also show that the strong ... In graph theory, a graph product is a binary operation on graphs. Specifically, it is an operation that takes two graphs G1 and G2 and produces a graph H with the following properties: • The vertex set of H is the Cartesian product V(G1) × V(G2), where V(G1) and V(G2) are the vertex sets of G1 and G2, respectively. • Two vertices (a1,a2) and (b1,b2) of H are connected by an edge, iff a condition about a1, b1 in G1 and a2, b2 in G2 is fulfilled. clock repair in kc