Bounds on Hosoya Index Involving Some Other Topological Indices

Abstract

For a graph \(G\), its Hosoya index is defined as the total number
of matchings in it, including the empty set. As one of the oldest and
well-studied molecular topological descriptors, the Hosoya index has
been extensively explored.

Notably, existing literature has primarily focused on its extremal
properties. In this note, we bridge a significant gap by establishing
sharp lower bounds for the Hosoya index in terms of other topological
indices.