Morphisms on middle graph of semiring valued graphs

Abstract

The middle graph M(G) of a graph G is an intersection graph on the vertex set V (G) of any graph G. Let E(G) be an edge set of G and F = V’ (G) ∪ E(G), where V’ (G) indicates the family of all one vertex subsets of the set V (G). This concept was introduced by T. Hamada and I. Yoshimura [4]. M. Chandramouleeswaran et al., studied isomorphism and automorphism groups for semiring valued graph (S-valued graph). In this paper, we study the morphisms and its properties of middle graph of S-valued graphs.