Properties of commuting graphs over semidihedral groups

Tao Cheng; Matthias Dehmer; Frank Emmert-Streib; Yongtao Li; Weijun Liu

doi:10.3390/sym13010103

Properties of commuting graphs over semidihedral groups

Tao Cheng
, Matthias Dehmer^*
, Frank Emmert-Streib
, Yongtao Li
, Weijun Liu

^*Corresponding author for this work

Shandong Normal University
Swiss Distance University of Applied Sciences
Nankai University
Xi'an Technological University
Private University for Health Sciences, Medical Informatics and Technology
Tampere University
Institute of Biosciences and Medical Technology
Hunan University
Central South University

Research output: Contribution to journal › Article › peer-review

Abstract

This paper considers commuting graphs over the semidihedral group SD_8n . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD_8n . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

Original language	English
Article number	103
Pages (from-to)	1-15
Number of pages	15
Journal	Symmetry
Volume	13
Issue number	1
DOIs	https://doi.org/10.3390/sym13010103
Publication status	Published - Jan 2021
Externally published	Yes

Keywords

Commuting graph
Graph spectrum
Semidihedral groups
Spectral radius

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10.3390/sym13010103

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title = "Properties of commuting graphs over semidihedral groups",

abstract = "This paper considers commuting graphs over the semidihedral group SD8n . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.",

keywords = "Commuting graph, Graph spectrum, Semidihedral groups, Spectral radius",

author = "Tao Cheng and Matthias Dehmer and Frank Emmert-Streib and Yongtao Li and Weijun Liu",

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year = "2021",

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doi = "10.3390/sym13010103",

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AU - Cheng, Tao

AU - Dehmer, Matthias

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AU - Li, Yongtao

AU - Liu, Weijun

PY - 2021/1

Y1 - 2021/1

N2 - This paper considers commuting graphs over the semidihedral group SD8n . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

AB - This paper considers commuting graphs over the semidihedral group SD8n . We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n ≥ 15 or even n ≥ 2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n . We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

KW - Commuting graph

KW - Graph spectrum

KW - Semidihedral groups

KW - Spectral radius

UR - https://www.scopus.com/pages/publications/85099180879

U2 - 10.3390/sym13010103

DO - 10.3390/sym13010103

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SN - 2073-8994

VL - 13

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JO - Symmetry

JF - Symmetry

IS - 1

M1 - 103

ER -

Properties of commuting graphs over semidihedral groups

Abstract

Keywords

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