Support Strong Degree Sequence in Fuzzy Graphs

Abstract

Let G=( ) be a fuzzy graph. Let u be an element of V. Let . The fuzzy support of u is defined as the sum of the neighbourhood degrees of the elements in N(u).Then the fuzzy support strong degree of u= It is denoted by deg s f(supp) (u). Arrange the support strong degrees of vertices of G in descending order. Let (d 1 ,d 2 ,……,d n ) with d i ≥d i+1 be the fuzzy support strong degree sequence of G. In this research work we introduce the concept of support strong degree sequence in fuzzy graphs.  The fuzzy support of a vertex is defined and domination based on the fuzzy support is considered. Several results involving this new fuzzy domination parameter are established.