Centered Polygonal Sum Labeling of Graphs

Abstract

Let G be a $(p,q)$ graph. A graph G admits centered polygonal sum labeling if a one to one function $f:V(G)\rightarrow N$ (where $N$ is a set of all non-negative integers) that induces a bijection $f^+: E(G)\rightarrow\{\mathbf{_CP_k(1)},\mathbf{_CP_k(2)},\cdots ,\mathbf{_CP_k(n)}\}$ of the edges of G defined by $f^+(uv) = f(u) + f(v)$ for every $e=uv \epsilon E(G),$ where $\mathbf{_CP_k(1)},\mathbf{_CP_k(2)},\cdots ,\mathbf{_CP_k(q)} $, $k\ge3$ are the first q centered polygonal numbers. A graph which admits such labeling is called centered polygonal sum graph. In this paper we characterize some families of graphs such as Path, Comb, Star graph, Subdivision of star, Bistar, $S_{m,n,r}$, Coconut tree admit centered polygonal sum labeling.