On some characterizations of strong power graphs of finite groups

A. K. Bhuniya; Sudip Bera

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 121-129
  • ISSN: 2300-7451

Abstract

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Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.

How to cite

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A. K. Bhuniya, and Sudip Bera. "On some characterizations of strong power graphs of finite groups." Special Matrices 4.1 (2016): 121-129. <http://eudml.org/doc/276590>.

@article{A2016,
abstract = {Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.},
author = {A. K. Bhuniya, Sudip Bera},
journal = {Special Matrices},
keywords = {groups; strong power graphs; line graphs; Laplacian spectrum; Laplacian permanent},
language = {eng},
number = {1},
pages = {121-129},
title = {On some characterizations of strong power graphs of finite groups},
url = {http://eudml.org/doc/276590},
volume = {4},
year = {2016},
}

TY - JOUR
AU - A. K. Bhuniya
AU - Sudip Bera
TI - On some characterizations of strong power graphs of finite groups
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 121
EP - 129
AB - Let G be a finite group of order n. The strong power graph Ps(G) of G is the undirected graph whose vertices are the elements of G such that two distinct vertices a and b are adjacent if am1=bm2 for some positive integers m1, m2 < n. In this article we classify all groups G for which Ps(G) is a line graph. Spectrum and permanent of the Laplacian matrix of the strong power graph Ps(G) are found for any finite group G.
LA - eng
KW - groups; strong power graphs; line graphs; Laplacian spectrum; Laplacian permanent
UR - http://eudml.org/doc/276590
ER -

References

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