Titre : [FORTHCOMING] Forests maximizing the Hosoya index with fixed size and matching number 

Auteurs : Rasamimanantsoa Victor,  

Revue : Advances in Pure and Applied Mathematics 

Numéro : Forthcoming papers<br> 

Volume :  

Date : 2026/10/14 

DOI : TBA 

ISSN : 1869-6090 

Résumé : The Hosoya index of a graph $$$G$$$ is defined as the total number of matchings in $$$G$$$, including the empty edge set. In this paper, we study the maximum value of the Hosoya index. To this end, we introduce the notion of a "balanced forest of stars" and we characterize all forests of size $$$n$$$ and matching number $$$m$$$ that maximize the Hosoya index. We prove that this maximum is attained if and only if the forest is a balanced forest of stars. 

Éditeur : ISTE OpenScience