The diameter of proper power graphs of alternating groups

Abstract

The power graph V{G) of finite group G is a simple graph whose vertex set is G and two distinct elements a and 0 are adjacent if and only if one of them is a power of the other. The proper power graph of G denoted by V(G) is a graph which is obtained by deleting the identity vertex (the identity element of G). In this paper, we improve the diameter bound of P'(An) for which P'(An) is connected. We show that 6 < diam(P'(A)) < 11 for n > 51. We also describe a number of short paths in these power graphs. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.