Results 1 to 10 of about 104,321 (158)
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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MultiGSA: wind power prediction based on a multi-scale cross-graph network combined with an enhanced simple attention mechanism [PDF]
Scientific ReportsWind power generation datasets are widely encountered in renewable energy systems because of their inherent periodicity, non-stationarity, and substantial noise.
Xufei Zhang +4 more
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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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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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Between the enhanced power graph and the commuting graph
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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The cyclic graph (deleted enhanced power graph) of a direct product [PDF]
Involve, a Journal of Mathematics, 2021 Let $G$ be a finite group. Define a graph on the set $G^{\#} = G \setminus \{ 1 \}$ by declaring distinct elements $x,y\in G^{\#}$ to be adjacent if and only if $\langle x,y\rangle$ is cyclic. Denote this graph by $Δ(G)$. The graph $Δ(G)$ has appeared in the literature under the names cyclic graph and deleted enhanced power graph.
Costanzo, David G. +4 more
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A survey on enhanced power graphs of finite groups
Electronic Journal of Graph Theory and Applications, 2022 Summary: We survey known results on enhanced power graphs of finite groups. Open problems, questions and suggestions for future work are also included.
Xuanlong Ma +3 more
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Enhanced power graphs of certain non-abelian groups
Discrete Mathematics, Algorithms and Applications, 2023 The enhanced power graph of a group [Formula: see text] is a simple undirected graph with vertex set [Formula: see text] and two vertices are adjacent if they belong to the same cyclic subgroup. In this paper, we obtain the Laplacian spectrum of the enhanced power graph of certain non-abelian groups, viz.
Parveen, Dalal, Sandeep, Kumar, Jitender
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On Difference of Enhanced Power Graph and Power Graph of a Finite Group
, 2022 28 ...
Biswas, Sucharita +3 more
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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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