Kemeny's constant and Kirchhoffian indices for a family of non-regular graphs

TL;DR

This paper derives explicit formulas for Kemeny's constant and Kirchhoffian indices for a class of composite graphs built from symmetric basic blocks, enhancing understanding of their structural properties.

Contribution

It introduces closed-form expressions linking Kemeny's constant with Kirchhoffian indices for non-regular graphs constructed from symmetric components.

Findings

Closed-form formulas for Kemeny's constant.

Relationships established between Kemeny's constant and Kirchhoffian indices.

Applicable to composite graphs with symmetry properties.

Abstract

We find closed form formulas for Kemeny's constant and its relationship with two Kirchhoffian indices for some composite graphs that use as basic building block a graph endowed with one of several symmetry properties.