The proof of a conjecture concerning acyclic molecular graphs with maximal Hosoya index and diameter 4

摘要

The Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we solve a conjecture in Ou, J. Math. Chem, DOI: 10.1007/S10910-006-9199-1 concerning acyclic molecular graphs with maximal Hosoya index and diameter 4.