PRODUCT OF TOTAL AND RANGE FUZZY EDGE LABELING OF CERTAIN GRAPH FAMILIES

Abstract

Fuzzy graph labeling deals with the assignment of membership values to the vertices and edges of a graph under prescribed constraints. In this paper, a product of total and range fuzzy edge labeling is introduced. A graph  is said to admit this labeling if there exist bijections  and  such that  and

for all . Graphs satisfying these conditions are identified as product of total and range fuzzy edge labeling graphs. Using this framework, it is shown that the path graph, cycle graph, friendship graph, triangular snake graph, triangular book, generalized butterfly graph, ladder graph and coconut tree graph admit such a labeling.