The structure and metric dimension of the power graph of a finite group
TLDR
This work first shows that P G has a transitive orientation, so it is a perfect graph and its core is a complete graph, and uses the poset on all cyclic subgroups of G (under usual inclusion) to characterize the structure of P G .About:
This article is published in European Journal of Combinatorics.The article was published on 2015-01-01 and is currently open access. It has received 66 citations till now. The article focuses on the topics: Graph power & Complement graph.read more
Citations
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Automorphism groups of supergraphs of the power graph of a finite group
Asma Hamzeh,Ali Reza Ashrafi +1 more
TL;DR: It is proved that the automorphism group of the main supergraphs and cyclic graphs can be written as a combination of Cartesian and wreath products of some symmetric groups.
Journal ArticleDOI
Recent developments on the power graph of finite groups - a survey
TL;DR: This paper aims to demonstrate the efforts towards in-situ applicability of EMMR-II, which aims to provide real-time information about the response of the immune system to EMTs.
Posted Content
The full automorphism group of the power (di)graph of a finite group
TL;DR: The full automorphism group of the power (di)graph of a finite group is described and a conjecture proposed by Doostabadi, Erfanian and Jafarzadeh in 2013 is solved.
Journal ArticleDOI
The strong metric dimension of the power graph of a finite group
TL;DR: In this paper, the authors characterized the strong metric dimension of the power graph of a finite group with respect to a cyclic group, an abelian group, a dihedral group and a generalized quaternion group.
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On the chromatic number of the power graph of a finite group
Xuanlong Ma,Min Feng +1 more
TL;DR: In this paper, the chromatic number χ ( Γ G ) of a finite group G is investigated and a characterization of χ( ΓG ) is presented, and a conjecture in Mirzargar et al. is disproved.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Algebraic Graph Theory
Chris Godsil,Gordon F. Royle +1 more
TL;DR: The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.
Book
Modern graph theory
TL;DR: This book presents an account of newer topics, including Szemer'edi's Regularity Lemma and its use; Shelah's extension of the Hales-Jewett Theorem; the precise nature of the phase transition in a random graph process; the connection between electrical networks and random walks on graphs; and the Tutte polynomial and its cousins in knot theory.