On Antimagic Total Labelings of Generalized Petersen Graph

Abstract

A total labeling of a graph $G$ with $p$ vertices and $q$ edges is a one-to-one mapping from $V(G)\cup E(G)$ onto $\{1,2,\dots ,p+q\}$. If the edge-weights (resp. vertex-weights) form an arithmetic progression starting from $a$ and having common difference $d$, then the labeling is called an $(a,d)$-edge (resp. vertex) – antimagic total labeling. In this paper, we consider such labeling applied to the generalized Petersen graph.