Commuting graph of CA−groups


  • Mehdi Torktaz Unversity of Kashan.
  • Ali Reza Ashrafi University of Kashan.



commuting graph, CA−group, distance, detour distance, metric dimension


A group G is called a CA−group, if all the element centralizers of G are abelian and the commuting graph of G with respect to a subset A of G, denoted by Γ(G, A), is a simple undirected graph with vertex set A and two distinct vertices a and b are adjacent if and only if ab = ba. The aim of this paper is to generalize results of a recently published paper of F. Ali, M. Salman and S. Huang [On the commuting graph of dihedral group, Comm. Algebra 44 (6) (2016) 2389—2401] to the case that G is an CA−group.

Author Biographies

Mehdi Torktaz, Unversity of Kashan.

Department of Pure Mathematics, Faculty of Mathematical Sciences.

Ali Reza Ashrafi, University of Kashan.

Department of Pure Mathematics, Faculty of Mathematical Sciences.


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How to Cite

M. Torktaz and A. R. Ashrafi, “Commuting graph of CA−groups ”, Proyecciones (Antofagasta, On line), vol. 42, no. 1, pp. 1-17, Jan. 2023.




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