Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.
In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|$. Moreover, we determine eccentric connectivity index of $Gamma_G$ for every non-abelian finite group $G$ in terms of the number of conjugacy classes $k(G)$ and the size of the group $G$.
Azad, A., & ELahinezhad, N. (2015). On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups. Caspian Journal of Mathematical Sciences, 4(1), 43-49.
MLA
A. Azad; N. ELahinezhad. "On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups", Caspian Journal of Mathematical Sciences, 4, 1, 2015, 43-49.
HARVARD
Azad, A., ELahinezhad, N. (2015). 'On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups', Caspian Journal of Mathematical Sciences, 4(1), pp. 43-49.
VANCOUVER
Azad, A., ELahinezhad, N. On the Szeged and Eccentric connectivity indices of non-commutative graph of finite groups. Caspian Journal of Mathematical Sciences, 2015; 4(1): 43-49.
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