Some applications of graph theory to finite groups

DOI10.1016/0012-365X(83)90004-3zbMath0506.05060MaRDI QIDQ1836678

Edward A. Bertram

Publication date: 1983

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

conjugacy classesindependence numberdegree sequencecentralizer vertex colouring

Mathematics Subject Classification ID

Graph theory (05C99) Commutator calculus (20F12)

Related Items (40)

On the Clique Numbers of Non-commuting Graphs of Certain Groups ⋮ Note on structural properties of graphs ⋮ Non-commuting graphs of rings ⋮ Three questions of Bertram on locally maximal sum-free sets ⋮ Centralizers in a group whose central factor is simple ⋮ ON MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS IN FINITE -GROUPS ⋮ On Non-commuting Sets in Certain Finite p-Groups ⋮ GROUP PERFECT CODE IN COMMUTING ORDER PRODUCT PRIME GRAPH ⋮ On the endomorphism semigroups of extra-special $p$-groups and automorphism orbits ⋮ Minimal covers of \(S_ n\) by Abelian subgroups and maximal subsets of pairwise noncommuting elements ⋮ MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF THREE-DIMENSIONAL GENERAL LINEAR GROUPS ⋮ Distances on the commuting graph of the ring of real matrices ⋮ Maximal non-commuting set in 2-generated p-groups of class two ⋮ Minimal paths in the commuting graphs of semigroups ⋮ Weighted graphs with an application to returned sequence ⋮ Degree polynomial for vertices in a graph and its behavior under graph operations ⋮ Metric Properties of Non-Commuting Graph Associated to Two Groups ⋮ On F-groups with the central factor of order p ⁴ ⋮ Abelian coverings of finite general linear groups and an application to their non-commuting graphs. ⋮ Groups containing locally maximal product-free sets of size 4 ⋮ A Generalization of Noncommuting Graph via Automorphisms of a Group ⋮ Maximal non-commuting sets in certain unipotent upper-triangular linear groups ⋮ The non-nilpotent graph of a semigroup. ⋮ Finite groups ⋮ Non-commuting graph of a group. ⋮ A generalization of Neumann's question ⋮ A combinatorial characterization of finite groups of prime exponent ⋮ On the non-commuting graph of dihedral group ⋮ Finite groups determined by the number of element centralizers ⋮ B.H. Neumann's Question on Ensuring Commutativity of Finite Groups ⋮ On groups covered by finitely many centralizers and domination number of the commuting graphs ⋮ On a Commuting Graph on Conjugacy Classes of Groups ⋮ On the three questions of Bertram on locally maximal sum-free sets ⋮ Intersection graphs of general linear groups ⋮ MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF SOME p-GROUPS OF MAXIMAL CLASS ⋮ Unnamed Item ⋮ Laplacian spectra of power graphs of certain finite groups ⋮ Inverse graphs associated with finite groups ⋮ The commuting graph of the symmetric inverse semigroup ⋮ The divisibility graph for F-groups

Cites Work

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• Group Ramsey theory
• Combinatorics. Room squares, sum-free sets, Hadamard matrices
• On Large Cyclic Subgroups of Finite Groups
• On coverings of a finite group by abelian subgroups
• Combinatorial Relations and Chromatic Graphs

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