On g-Noncommuting Graph of a Finite Group Relative to Its Subgroups
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Let H be a subgroup of a finite non-abelian group G and g∈G. Let Z(H,G)={x∈H:xy=yx,∀y∈G}. We introduce the graph ΔH,Gg whose vertex set is G\Z(H,G) and two distinct vertices x and y are adjacent if x∈H or y∈H and [x,y]≠g,g−1, where [x,y]=x−1y−1xy. In this paper, we determine whether ΔH,Gg is a tree among other results. We also discuss about its diameter and connectivity with special attention to the dihedral groups.
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2016 ◽
Vol 15
(07)
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pp. 1650127
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2019 ◽
Vol 12
(05)
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pp. 1950081
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1964 ◽
Vol 16
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pp. 485-489
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