On the difference of the enhanced power graph and the power graph of a finite group

Biswas, S and Cameron, PJ and Das, A and Dey, HK (2024) On the difference of the enhanced power graph and the power graph of a finite group. In: Journal of Combinatorial Theory. Series A, 208 .

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Abstract

The difference graph D(G) of a finite group G is the difference of the enhanced power graph of G and the power graph of G, where all isolated vertices are removed. In this paper we study the connectedness and perfectness of D(G) with respect to various properties of the underlying group G. We also find several connections between the difference graph of G and the Gruenberg-Kegel graph of G. We also examine the operation of twin reduction on graphs, a technique which produces smaller graphs which may be easier to analyze. Applying this technique to simple groups can have a number of outcomes, not fully understood, but including some graphs with large girth. © 2024 Elsevier Inc.

Item Type:	Journal Article
Publication:	Journal of Combinatorial Theory. Series A
Publisher:	Academic Press Inc.
Additional Information:	The copyright for this article belongs to Elsevier.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics
Date Deposited:	30 Jul 2024 05:15
Last Modified:	30 Jul 2024 05:15
URI:	http://eprints.iisc.ac.in/id/eprint/85688

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