Publication

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 a labeling 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 are found.