Certain product set labeling of graphs and their cardinality

Abstract

A product set-labeling of a graph G is an injective function f: V (G) →P(N) such that the induced edge function f: E(G) →P(N)defined by f*(uv) = f(u)*f(v) is injective. A product set labeling of a graph G is a geometric product set labeling if the set labels of all its elements, that is vertices and edges with respect to the function f are geometric progressions.The number of elements in the set label of a vertex or edge of a graph G is called its cardinality.In this paper, we have found alabeling in which all the edges of a graph G are in geometric progressions even though the set labels of one of its vertex is not a geometric progression. Also the edge cardinalty of such graphs.