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On the difference of the enhanced power graph and the power graph of a finite group
Journal of Combinatorial Theory - Series A, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Peter J Cameron, Angsuman Das
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The power graph of a torsion-free group determines the directed power graph [PDF]
Discrete Applied Mathematics, 2021 The directed power graph $\vec{\mathcal G}(\mathbf G)$ of a group $\mathbf G$ is the simple digraph with vertex set $G$ such that $x\rightarrow y$ if $y$ is a power of $x$. The power graph of $\mathbf G$, denoted with $\mathcal G(\mathbf G)$, is the underlying simple graph. In this paper, for groups $\mathbf G$ and $\mathbf H$, the following is proved.
Samir Zahirovic
exaly +4 more sources
A Review of Graph Neural Networks and Their Applications in Power Systems
Journal of Modern Power Systems and Clean Energy, 2022 Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks are typically represented in Euclidean domains.
Wenlong Liao +4 more
doaj +3 more sources
Power Graphs Defined on Non-Commutative Non-Associative Moufang Loops [PDF]
Advances in Group Theory and Applications, 2023 For a non-abelian group G of order n and for an odd prime p we present the non-commutative non-associative Moufang loop M = Mpn(G, p) of order pn. We name this loop the generalized Chein loop in celebrating the Chein loop defined in 1974 by Orin Chein ...
Fatemeh Samnia, Yadollah Marefat
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Planarity of Inclusion Graph of Cyclic Subgroups of Finite Group [PDF]
Mathematics Interdisciplinary Research, 2020 Let G be a finite group. The inclusion graph of cyclic subgroups of G, Ic(G), is the (undirected) graph with vertices of all cyclic subgroups of G, and two distinct cyclic subgroups ⟨a⟩ and ⟨b⟩, are adjacent if and only if ⟨a⟩ ⊂ ⟨b⟩ or ⟨b⟩ ⊂ ⟨a⟩. In this
Zahra Garibbolooki, Sayyed Heidar Jafari
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Descending endomorphism graphs of groups
AKCE International Journal of Graphs and Combinatorics, 2023 We define a new type of graph of a group with reference to the descending endomorphisms of the group. A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. We define the
Vinay Madhusudanan +2 more
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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
Cauchy: Jurnal Matematika Murni dan Aplikasi, 2023 Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph.
Evi Yuniartika Asmarani +5 more
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Graph Powers and Graph Homomorphisms [PDF]
The Electronic Journal of Combinatorics, 2010 In this paper, we investigate some basic properties of fractional powers. In this regard, we show that for any non-bipartite graph $G$ and positive rational numbers ${2r+1\over 2s+1} < {2p+1\over 2q+1}$, we have $G^{2r+1\over 2s+1} < G^{2p+1\over 2q+1}$. Next, we study the power thickness of $G$, that is, the supremum of rational numbers ${2r+
Hossein Hajiabolhassan, Ali Taherkhani
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Permutational Powers of a Graph [PDF]
The Electronic Journal of Combinatorics, 2019 This paper introduces a new graph construction, the permutational power of a graph, whose adjacency matrix is obtained by the composition of a permutation matrix with the adjacency matrix of the graph. It is shown that this construction recovers the classical zig-zag product of graphs when the permutation is an involution, and it is in fact more ...
Matteo Cavaleri +2 more
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Forbidden Subgraphs of Power Graphs [PDF]
The Electronic Journal of Combinatorics, 2021 The undirected power graph (or simply power graph) of a group $G$, denoted by $P(G)$, is a graph whose vertices are the elements of the group $G$, in which two vertices $u$ and $v$ are connected by an edge between if and only if either $u=v^i$ or $v=u^j$ for some $i$, $j$.
Pallabi Manna +2 more
openaire +5 more sources