DIAMOND PRODUCT OF TWO COMMONCOMPLETE BIPARTITE GRAPHS

摘要

A homomorphism of a graph G = (V, E) into a graph H = (V', E') is a mapping f : V→ V' which preserves edges: for all x, y E V, if {x, y} ∈ E, then {f(x), f(y)} ∈ E'. Let Hom(G,H) be the class of all homomorphisms from graph G into graph H. The diamond product of a graph G = (V, E) with a graph H = (V', E') (denoted by G o H) is a graph defined by the vertex set V (G o H) = Hom(G, H) and the edge set E(G o H) = {{ f, g} ∈ H om(G , H)|{f (x), g(x)} E E' for all x ∈ V}. Let K_(m,n) be a complete bipartite graph on m+n vertices. This research aims to study the diamond product of two common complete bipartite graphs K_(m,n). We find that the resulting graph is also a complete bipartite graph on m~m n~n n~m m~n vertices with diameter equal to two.