Bulletin of the Iranian Mathematical Society, ( ISI ), Volume (39), No (4), Year (2013-8) , Pages (663-674)

Title : ( Relative n-th non-commuting graphs of finite groups )

Authors: Ahmad Erfanian , Behnaz Tolue Haghighi ,

Citation: BibTeX | EndNote

Suppose n is a fxed positive integer. We introduce the relative n-th non-commuting graph n H;G, associated to the non-abelian subgroup H of group G. The vertex set is G n Cn H;G in which Cn H;G = fx 2 G : [x; yn] = 1 and [xn; y] = 1 for all y 2 Hg. Moreover, fx; yg is an edge if x or y belong to H and xyn = ynx or xny = yxn. In fact, the relative n-th commutativity degree, Pn(H;G) the probability that n-th power of an element of the sub- group H commutes with another random element of the group G and the non-commuting graph are the keys to construct such a graph. It is proved that two isoclinic non-abelian groups have iso- morphic graphs under special conditions.

Keywords

, Isoclinism, n-th non-commuting graph, n-th commutativity
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@article{paperid:1052641,
author = {Erfanian, Ahmad and Tolue Haghighi, Behnaz},
title = {Relative n-th non-commuting graphs of finite groups},
journal = {Bulletin of the Iranian Mathematical Society},
year = {2013},
volume = {39},
number = {4},
month = {August},
issn = {1735-8515},
pages = {663--674},
numpages = {11},
keywords = {Isoclinism; n-th non-commuting graph; n-th commutativity degree},
}

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%0 Journal Article
%T Relative n-th non-commuting graphs of finite groups
%A Erfanian, Ahmad
%A Tolue Haghighi, Behnaz
%J Bulletin of the Iranian Mathematical Society
%@ 1735-8515
%D 2013

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