The Hosoya polynomial of distance-regular graphs

TL;DR

This paper derives an explicit formula for the Hosoya polynomial of distance-regular graphs, including strongly regular graphs, using their intersection array, simplifying the computation of this graph invariant.

Contribution

It provides a new explicit formula linking the Hosoya polynomial to the intersection array of distance-regular graphs, including strongly regular graphs.

Findings

Explicit formula for Hosoya polynomial of distance-regular graphs

Simplified formula for strongly regular graphs

Facilitates easier computation of Hosoya polynomial

Abstract

In this note we obtain an explicit formula for the Hosoya polynomial of any distance-regular graph in terms of its intersection array. As a consequence, we obtain a very simple formula for the Hosoya polynomial of any strongly regular graph.