Energy, Hosoya index and Merrifield–Simmons index of trees with prescribed degree sequence

Abstract

The energy of a graph, defined as the sum of the absolute values of its eigenvalues, the number of independent edge subsets (known as Hosoya index) and the number of independent vertex subsets (called Merrifield–Simmons index) are three closely related graph invariants that are studied in mathematical chemistry. In this paper, we characterize the unique (up to isomorphism) tree which has a given degree sequence, minimum energy and Hosoya index and maximum Merrifield–Simmons index. We also compare different degree sequences and show how various known results follow as simple corollaries from our main theorem.