Graceful labeling of power graph of group Zk−12×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 G=Zk−12×Z4 be a finite abelian 2-group of order 2k+1 where k≥1. In this paper, we establish that the power graph of finite abelian group G always has graceful labeling without any condition on k.
Communicated by I. Peterin