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

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.