Results 11 to 20 of about 96,720 (286)
On the difference of the enhanced power graph and the power graph of a finite group [PDF]
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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On spectrum and energies of enhanced power graphs
Mathematics OpenThe enhanced power graph [Formula: see text] of a group G is a simple graph with vertex set G and two distinct vertex are adjacent if and only if they belong to the same cyclic subgroup.
Pankaj Kalita, Prohelika Das
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Certain properties of the enhanced power graph associated with a finite group
Acta Mathematica Hungarica, 2023 The enhanced power graph of a finite group $G$, denoted by $\mathcal{P}_E(G)$, is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of $\mathcal{P}_E(
Jitendra Kumar
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Between the enhanced power graph and the commuting graph [PDF]
Journal of Graph Theory, 2022 AbstractThe purpose of this note is to define a graph whose vertex set is a finite group , whose edge set is contained in that of the commuting graph of and contains the enhanced power graph of . We call this graph the deep commuting graph of . Two elements of are joined in the deep commuting graph if and only if their inverse images in every central ...
Peter J. Cameron, Bojan Kuzma
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An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
Acta Mathematica Hungarica11 pages, Comments are welcome.
Bera, S., Dey, H. K.
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On the Structure of the Power Graph and the Enhanced Power Graph of a Group
The Electronic Journal of Combinatorics, 2017 Let $G$ be a group. The power graph of $G$ is a graph with the vertex set $G$, having an edge between two elements whenever one is a power of the other. We characterize nilpotent groups whose power graphs have finite independence number. For a bounded exponent group, we prove its power graph is a perfect graph and we determine its clique ...
Ghodratollah Aalipour +4 more
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The rainbow connection number of the enhanced power graph of a finite group
Electronic Journal of Graph Theory and Applications, 2023 Let G be a finite group. The enhanced power graph ΓGe of G is the graph with vertex set G and two distinct vertices are adjacent if they generate a cyclic subgroup of G. In this article, we calculate the rainbow connection number of ΓGe.
Luis A. Dupont +2 more
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On the Connectivity of Enhanced Power Graphs of Finite Groups
Graphs and Combinatorics, 2021 This paper deals with the vertex connectivity of enhanced power graph of finite group. We classify all abelian groups G such that vertex connectivity of enhanced power graph of G is 1. We derive an upper bound of vertex connectivity for the enhanced power graph of any general abelian group G.
Sudip Bera +2 more
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Perfect codes in power graphs of finite groups
Open Mathematics, 2017 The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the ...
Ma Xuanlong +4 more
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Distance matrix of enhanced power graphs of finite groups
, 2023 The enhanced power graph of a group $G$ is the graph $\mathcal{G}_E(G)$ with vertex set $G$ and edge set $ \{(u,v): u, v \in \langle w \rangle,~\mbox{for some}~ w \in G\}$. In this paper, we compute the spectrum of the distance matrix of the enhanced power graph of non-abelian groups of order $pq$, dihedral groups, dicyclic groups, elementary abelian ...
Arora, Anita +2 more
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