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Groups with maximum vertex degree commuting graphs
Publication details: New Delhi Springer 2024Edition: Vol.55(1), MarDescription: 234-241pSubject(s): Online resources: In: Indian journal of pure and applied mathematicsSummary: Let G be a finite non-abelian group and Z(G) be its center. We associate a commuting graph to G, whose vertex set is and two distinct vertices are adjacent if they commute. In this paper we prove that the set of all non-abelian groups whose commuting graph has maximum vertex degree bounded above by a fixed is finite. Also, we characterize all groups for which the associated commuting graphs have maximum vertex degree at most 4.| Item type | Current library | Status | Barcode | |
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School of Engineering & Technology Archieval Section | Not for loan | 2024-1562 |
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Let G be a finite non-abelian group and Z(G) be its center. We associate a commuting graph to G, whose vertex set is and two distinct vertices are adjacent if they commute. In this paper we prove that the set of all non-abelian groups whose commuting graph has maximum vertex degree bounded above by a fixed is finite. Also, we characterize all groups for which the associated commuting graphs have maximum vertex degree at most 4.
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