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

TL;DR

This paper calculates the exact distance spectral radius, forwarding index, and topological indices of the complement of specific circulant networks, enhancing understanding of their spectral and topological properties.

Contribution

It provides explicit formulas for spectral and topological indices of the complement of certain circulant networks, a novel contribution in network spectral analysis.

Findings

Exact values for distance spectral radius of network complements

Formulas for vertex-forwarding index in these networks

Computed distance-based topological indices

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.