On magic and antimagic total labeling of generalized Petersen graph

Abstract

A total labeling on a graph G with p vertices and q edges is a one-to-one function from V(G) ∪ E(G) onto the set of integers 1,2, ⋯, p+q. If the sum of the label on an edge and the labels of its endpoints is constant independent choice of edge, then the labeling is called edge-magic total labeling, and if the edge-weights form an arithmetic progression starting from a and having common difference d, then the labeling is called (a,d)-edge-antimagic total labeling. These labelings were introduced by Kotzig and Rosa (1970) and Simanjuntak et al (2000), respectively. This paper considers such a labeling applied to generalized Petersen graphs.