The complement of proper power graphs of finite groups

Anitha, T., Rajkumar, R. and Gagarin, Andrei ORCID: https://orcid.org/0000-0001-9749-9706 2018. The complement of proper power graphs of finite groups. Palestine Journal of Mathematics 7 (2) , pp. 579-597.

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Abstract

For a finite group G, the proper power graph P ∗ (G) of G is the graph whose vertices are non-trivial elements of G and two vertices u and v are adjacent if and only if u 6= v and u m = v or v m = u for some positive integer m. In this paper, we consider the complement of P ∗ (G), denoted by P∗(G). We classify all finite groups whose complement of proper power graphs is complete, bipartite, a path, a cycle, a star, claw-free, triangle-free, disconnected, planar, outerplanar, toroidal, or projective. Among the other results, we also determine the diameter and girth of the complement of proper power graphs of finite groups.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Mathematics
Publisher:	Palestine Polytechnic University
ISSN:	2219-5688
Date of First Compliant Deposit:	17 January 2018
Date of Acceptance:	15 December 2017
Last Modified:	15 Nov 2024 14:00
URI:	https://orca.cardiff.ac.uk/id/eprint/108229

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