On the regularity of a graph related to conjugacy classes of groups: small valencies
Capitolo di libro
Data di Pubblicazione:
2014
Citazione:
On the regularity of a graph related to conjugacy classes of groups: small valencies / M. Bianchi, M. Herzog, E. Pacifici (CONTEMPORARY MATHEMATICS). - In: Group theory, combinatorics, and computing / [a cura di] R. F. Morse, D. Nikolova-Popova, S. Witherspoon. - Providence : American Mathematical Society, 2014. - ISBN 9780821894354. - pp. 1-7 (( convegno International Conference in Honor of Daniela Nikolova-Popova's 60th Birthday on Group Theory, Combinatorics and Computing tenutosi a Boca Raton nel 2012 [10.1090/conm/611/12203].
Abstract:
Given a finite group G, denote by Gamma(G) the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of G, and set two vertices of Gamma(G) to be adjacent if and only if they are not coprime numbers. In this note we prove that, if Gamma(G) is a k-regular graph and either G is an F-group or k <= 5, then Gamma(G) is a complete graph with k + 1 vertices.
Tipologia IRIS:
03 - Contributo in volume
Keywords:
Finite groups; conjugacy class sizes; classes graphs; F-groups
Elenco autori:
M. Bianchi, M. Herzog, E. Pacifici
Link alla scheda completa:
Titolo del libro:
Group theory, combinatorics, and computing