On the non-commuting graph of dihedral group

Sanhan Muhammad Salih Khasraw, Ivan Dler Ali, Rashad Rashid Haji


For a nonabelian group G, the non-commuting graph Γ of G is defined as the graph with vertex-set G-Z(G), where Z(G) is the center of G, and two distinct vertices of Γ are adjacent if they do not commute in G. In this paper, we investigate the detour index, eccentric connectivity and total eccentricity polynomials of the non-commuting graph on D2n. We also find the mean distance of the non-commuting graph on D2n.


dihedral group, non-commuting graph, detour distance, mean distance

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DOI: http://dx.doi.org/10.5614/ejgta.2020.8.2.3


A. Abdollahi, S. Akbari, and H.R. Maimani, Non-commuting graph of a group, J. Algebra 298 (2006), 468--492.

M.R. Alfuraidan and Y.F. Zakariya, Inverse graphs associated with finite groups, Electron. J. Graph Theory Appl. 5 (1) (2017), 142--154.

F. Ali, M. Salman and S. Huang, On the commuting graph of dihedral group, Comm. Algebra 44 (6) (2016), 2389--2401.

I. Althofer, Average distances in undirected graphs and the removal of vertices, J. Combin. Theory Ser. B 48 (1) (1990), 140--142.

H.J. Bandelt and H.M. Mulder, Distance-hereditary graphs, J. Combin. Theory Ser. B 41 (2) (1986), 182--208.

S. Bera, On the intersection power graph of a finite group, Electron. J. Graph Theory Appl. 6 (1) (2018), 178--189.

E.A. Bertram, Some applications of graph theory to finite groups, Discrete Math. 44 (1) (1983), 31--43.

E.A. Bertram, M. Herzog, and A. Mann, On a graph related to conjugacy classes of groups, Bull. Lond. Math. Soc. 22 (6) (1990), 569--575.

D. Bienstock and E. Gyori, Average distance in graphs with removed elements, J. Graph Theory 12 (3) (1988), 375--390.

T. Doslic, M. Ghorbani, and M.A. Hosseinzadeh, Eccentric connectivity polynomial of some graph operations, Util. Math. 84 (2011), 197--209.

R.J. Shahkoohi, O. Khormali, and A. Mahmiani, The polynomial of detour index for a graph, World Applied Sciences Journal 15 (10) (2011), 1473--1483.

E. Vatandoost and M. Khalili, Domination number of the non-commuting graph of finite groups, Electron. J. Graph Theory Appl. 6 (2) (2018), 228--237.


ISSN: 2338-2287

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