Anitha, T., Rajkumar, R. and Gagarin, Andrei ![]() ![]() |
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Official URL: http://pjm.ppu.edu/paper/476
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 |
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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: | 16 Nov 2023 22:53 |
URI: | https://orca.cardiff.ac.uk/id/eprint/108229 |
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