Super Pair Sum Labeling of $H$-graphs

Abstract

Let $G$ be a graph with $p$ vertices and $q$ edges.The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)\cup E(G)$ to $\left\{0,\pm1,\pm2,\dots,\pm\left(\frac{p+q-1}{2}\right)\right\}$ when $p+q$ is odd and from $V(G)\cup E(G)$ to $\left\{\pm1,\pm2,\dots,\pm\left(\frac{p+q}{2}\right)\right\}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a super pair sum graph. In this paper, we investigate super pair sum labeling of some $H$-graphs.