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.
@article{bwmeta1.element.doi-10_1515_spma-2016-0012,
author = {A. K. Bhuniya and Sudip Bera},
title = {On some characterizations of strong power graphs of finite groups},
journal = {Special Matrices},
volume = {4},
year = {2016},
pages = {121-129},
zbl = {1331.05136},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0012}
}
A. K. Bhuniya; Sudip Bera. On some characterizations of strong power graphs of finite groups. Special Matrices, Tome 4 (2016) pp. 121-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_spma-2016-0012/
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