Raquiel López
Facultad de Matem\'aticas, Universidad Veracruzana, Circuito Gonzalo Aguirre Beltr\'an S/N; Zona Universitaria; Xalapa, Ver., M\'exico, CP 91090

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The rainbow k-connectivity of the non-commutative graph of a finite group Luis A. Dupont; Raquiel López; Miriam Rodríguez
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.1.7

Abstract

The non-commuting graph Γ(G) of a non-abelian group G is defined as follows. The vertex set V(Γ(G)) of ℾ(G) is G \ Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ≠ yx. We prove that the rainbow k-connectivity of Γ(G) is equal to ⌈k/2⌉ + 2, for 3 ≤ k ≤ |Z(G)|.