Power graphs: A survey
Jemal H. Abawajy,Andrei V. Kelarev,Morshed U. Chowdhury +2 more
- Vol. 1, Iss: 2, pp 125-147
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This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature.Abstract:
This article gives a survey of all results on the power graphs of groups and semigroups obtained in the literature. Various conjectures due to other authors, questions and open problems are also included.read more
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Book ChapterDOI
Graphs and Digraphs
TL;DR: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element, so for any given data element or node in the list structure, the authors can talk in terms of a next element and a previous element.
Journal ArticleDOI
The structure and metric dimension of the power graph of a finite group
TL;DR: 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 .
Journal ArticleDOI
Certain properties of the power graph associated with a finite group
TL;DR: The power graph of a group G is a simple graph whose vertex-set is G and two vertices x and y in G are adjacent if and only if one of them is a power of the other as mentioned in this paper.
Journal ArticleDOI
Certain properties of the power graph associated with a finite group
TL;DR: In this article, the authors investigated the relation between the structure of directed or undirected graphs and the properties of groups in terms of some properties of the associated graph, and showed that many finite groups such as finite simple groups, symmetric groups and the automorphism groups of sporadic simple groups can be uniquely determined by their power graphs among all finite groups.
Journal ArticleDOI
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.
References
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Rees matrix constructions for clustering of data
TL;DR: A complete description of the error-correcting capabilities of a large family of clusterers based on Rees matrix semigroups well known in semigroup theory is given.
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On d-antimagic labelings of plane graphs
Martin Bača,Ljiljana Brankovic,Marcela Lascsáková,Oudone Phanalasy,Andrea Semanicova-Fenovciova +4 more
TL;DR: The paper examines the existence of such labelings for several families of plane graphs in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face.
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On congruences of automata defined by directed graphs
TL;DR: This work considers automata defined by graph algebras of directed graphs, characterize all congruences on these automata, and gives a complete description of all automata of this type satisfying three properties for congruence.
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Graceful Labelling: State of the Art, Applications and Future Directions
TL;DR: This paper describes applications of graceful and graceful-like labellings of trees to several well known combinatorial problems and exposes yet another one, namely the connection between α-labelling of paths and near transversals in Latin squares.