On M-strong fuzzy graphs

The cartesian product and disjoint sum of graphs play a prominent role and have numerous interesting algebraic properties. In this note, we consider operations on fuzzy graphs under which M-strong property is preserved. If G(1) and G(2) are M-strong fuzzy graphs then we prove that G(1) x G(2), G(1)[G(2)] and G(1) + G(2) are also M-strong but G(1) boolean OR G(2) need not be M-strong. If G(1) x G(2) is M-strong then we show that at least one factor must be M-strong. We show that the product of a M-strong fuzzy graph G(1) with a non-M-strong fuzzy graph G(2) remains M-strong if and only if G(2) satisfies special condition. For any fuzzy graph G, G(Cc) is the smallest M-strong fuzzy graph that contains G and G = G(Cc) if and only if G is M-strong. We further show that M-strong fuzzy graph G is a fuzzy tree if and only if the support(G) is a tree. (C) 2003 Elsevier Inc. All rights reserved.