Distance Eigenvalues, Forwarding Indices, and Distance-based Topological Indices of Complement of Two Circulant Networks

Abstract

Let $n$ and $a$ be positive integers such that $2\leq a\leq \frac{n}{2}$. In this short note, we compute for the exact value of the distance spectral radius, vertex-forwarding index, and some distance-based topological indices of the complement of circulant networks $C_n(1,a)$ and $C_{m^h}(1,m,m^2,\ldots,m^{h-1})$. For $a\neq \frac{n}{2}$, the circulant $C_n(1,a)$ is called a double loop network while the circulant $C_{m^h}(1,m,m^2,\ldots,m^{h-1})$ is called the multiplicative circulant network on $m^h$ vertices.