### On the non-commuting graph of dihedral group

#### Abstract

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 *D*_{2n}. We also find the mean distance of the non-commuting graph on *D*_{2n}.

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

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