THE EXISTENCE OR NONEXISTENCE OF NON-COMMUTING GRAPHS WITH PARTICULAR PROPERTIES
2013 ◽
Vol 13
(01)
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pp. 1350064
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Keyword(s):
We consider the non-commuting graph ∇(G) of a non-abelian finite group G; its vertex set is G\Z(G), the set of non-central elements of G, and two distinct vertices x and y are joined by an edge if [x, y] ≠ 1. We determine the structure of any finite non-abelian group G (up to isomorphism) for which ∇(G) is a complete multipartite graph (see Propositions 3 and 4). It is also shown that a non-commuting graph is a strongly regular graph if and only if it is a complete multipartite graph. Finally, it is proved that there is no non-abelian group whose non-commuting graph is self-complementary and n-cube.
2019 ◽
Vol 12
(05)
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pp. 1950081
Keyword(s):
2013 ◽
Vol 7
(1)
◽
pp. 119-128
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2018 ◽
Vol 17
(04)
◽
pp. 1850070
Keyword(s):
2016 ◽
Vol 15
(07)
◽
pp. 1650127
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Keyword(s):
Keyword(s):
2015 ◽
Vol 07
(04)
◽
pp. 1550060