$k$-geometric graphs

Abstract

A finite, simple and undirected graph G = (V, E) with p vertices and q edges is said to be a k-geometric mean graph for a positive integer k if there is an injection ψ :The special case k = 1, a 1-geometric mean labeling is called a geometric mean labeling, and a 1-geometric mean graph is called a geometric mean graph.In this paper, we present new classes of geometric mean graphs. Then we introduce k-geometric mean labeling and prove some classes of graphs are k-geometric mean. We also study some classes of finite join of graphs that admit geometric mean labeling.