@ARTICLE{TBA, 

TITLE={[FORTHCOMING] Forests maximizing the Hosoya index with fixed size and matching number}, 
  
AUTHOR={Rasamimanantsoa Victor, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={}, 

NUMBER={Forthcoming papers<br>}, 
	
YEAR={2026}, 

URL={https://www.openscience.fr/Forests-maximizing-the-Hosoya-index-with-fixed-size-and-matching-number}, 
	
DOI={TBA}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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.}}