Even vertex Oblong Mean Labeling of Subdivision of Some Connected Graphs

Abstract

The nth oblong number is denoted by On and is defined by On = n (n + 1) . Let G = (V, E) be a loop-free, not  having multiple edges, finite, and non-directed graphwith |V(G)| = p and |E(G)| = q. An even vertex oblong mean labeling is an injective function where Oq is the qth oblong number that induces a bijective edge labeling defined by for all e = uv ∈E(G). Every graph that accommodates evenvertex oblong mean labeling is called an evenvertex oblong mean graph. In the context of this paper, evenvertex oblong mean labeling of subdivision of a few path embraced graphs and some rooted trees are studied.