Distance Eigenvalues and Forwarding Indices of Multiplicative Circulant Graph of Order Power of Two and Three

TL;DR

This paper analyzes the distance eigenvalues and forwarding indices of multiplicative circulant graphs of order powers of two and three, providing explicit spectral and forwarding index values and bounds.

Contribution

It introduces a method to compute the distance matrix and spectral properties of these specific circulant graphs, including new bounds for forwarding indices.

Findings

Distance matrices and diameters determined for the graphs

Exact distance spectral radii and average distances calculated

Vertex-forwarding indices explicitly computed and bounds for edge-forwarding indices provided

Abstract

In this paper, we use Breadth-first search algorithm to determine the distance matrix of multiplicative circulant graph of order power of two and three. As a consequence, the diameter of the graphs were determined. We also give their distance spectral radii, average distances, as well as the exact values of vertex-forwarding indices. Finally, using some known relationships between the distance spectral radii and forwarding indices of a graph, we give some bounds for their edge-forwarding indices.