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.
Veena Vincent and Supriya Rajendran, “Certain Product Set Labeling Of Graphs And Their Cardinality”, International Journal of Recent Technology and Engineering , vol. 8, no. 1, 2019.