Graceful labeling of power graph of group Z2k−1 × Z4

Abstract

The power graph of a finite group G is a special type of undirected simple graph whose vertex set is set of elements of G, in which two distinct vertices of G are adjacent if one is the power of other. Let [Formula: see text] be a finite abelian 2-group of order [Formula: see text] where [Formula: see text]. In this paper, we establish that the power graph of finite abelian group G always has graceful labeling without any condition on [Formula: see text].