Mathématiques > Accueil > Avancées en Mathématiques Pures et Appliquées > Articles à paraître > Article
Rasamimanantsoa Victor
Université d’Antananarivo
Madagascar
Validé le 13 octobre 2026 DOI : À venir
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.
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.
