Results 131 to 140 of about 104,321 (158)

Enhanced power graphs are weakly perfect

Australas. J Comb., 2023
Summary: A graph is weakly perfect if its clique number and chromatic number are equal. We show that the enhanced power graph of a finite group \(G\) is weakly perfect: its clique number and chromatic number are equal to the maximum order of an element of \(G\). The proof requires a combinatorial lemma. We give some remarks about related graphs.
Peter J. Cameron, Veronica Phan
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On the structure of finite groups with dominatable enhanced power graph

Journal of Algebra and Its Applications, 2021
Let [Formula: see text] be a group. The enhanced power graph of [Formula: see text] is a graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if there exists [Formula: see text] such that [Formula: see text] and [Formula: see text] for some [Formula: see text]. Also, a vertex of a
Mahmoudifar, A., Babai, A.
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On enhanced power graphs of finite groups

Journal of Algebra and Its Applications, 2018
Given a group [Formula: see text], the enhanced power graph of [Formula: see text], denoted by [Formula: see text], is the graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are edge connected in [Formula: see text] if there exists [Formula: see text] such that [Formula: see text] and ...
Bera, Sudip, Bhuniya, A. K.
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Forbidden subgraphs in enhanced power graphs of finite groups

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas
The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold.
Samir Zahirović, Yanhong She, Xuanlong Ma   +2 more
exaly   +4 more sources

A study of enhanced power graphs of finite groups

Journal of Algebra and Its Applications, 2019
The enhanced power graph [Formula: see text] of a group [Formula: see text] is the graph with vertex set [Formula: see text] such that two vertices [Formula: see text] and [Formula: see text] are adjacent if they are contained in the same cyclic subgroup.
Zahirović, Samir, Bošnjak, Ivica, Madaras-Silađi, Rozalija   +2 more
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The metric dimension of the enhanced power graph of a finite group

Journal of Algebra and Its Applications, 2019
The enhanced power graph of a finite group [Formula: see text] is the graph whose vertex set is [Formula: see text], and two distinct vertices are adjacent if they generate a cyclic subgroup of [Formula: see text]. In this paper, we establish an explicit formula for the metric dimension of an enhanced power graph.
Ma, Xuanlong, She, Yanhong
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A graph model for enhancing situational awareness in power systems

2017 19th International Conference on Intelligent System Application to Power Systems (ISAP), 2017
As societies are becoming more dependent on the power grids, the security issues and blackout threats are more emphasized. This paper proposes a new graph model for online visualization and assessment of power grid security. The proposed model integrates topology and power flow information to estimate and visualize interdependencies between the lines ...
Mirjavad Hashemi Gavgani, Sara Eftekharnejad   +1 more
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Graph-enhanced fault hierarchical perception for Dissolved Gas Analysis in power transformer

Engineering Applications of Artificial Intelligence
Huifang Ma
exaly   +3 more sources

An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups

Acta Mathematica Hungarica
11 pages, Comments are welcome.
Bera, S., Dey, H. K.
exaly   +3 more sources

Characteristics of the Enhanced Power Coprime Graphs of Some Finite Groups

Malaysian Journal of Mathematical Sciences
The graphs of groups is a powerful tool for studying finite groups as it visually represents their structures and relationships. In general, introducing new graphs of groups leads to discoveries about the graphs' characteristics, offering significant insights into its structure, connectivity, and spectral aspects.
N. Mohamed, N. M. Mohd Ali, M. Bello
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