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The complement of proper power graphs of finite groups

Anitha, T., Rajkumar, R. and Gagarin, Andrei 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: Mathematics
Publisher: Palestine Polytechnic University
ISSN: 2219-5688
Date of First Compliant Deposit: 17 January 2018
Date of Acceptance: 15 December 2017
Last Modified: 18 Oct 2019 05:12
URI: http://orca-mwe.cf.ac.uk/id/eprint/108229

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