On the ordering of graphs with respect to their matching numbers
Discrete Applied Mathematics
Graphs, partitions and Fibonacci numbers
Discrete Applied Mathematics
Maximizing the number of independent subsets over trees with bounded degree
Journal of Graph Theory
The extremal values of the Wiener index of a tree with given degree sequence
Discrete Applied Mathematics
The signless Laplacian spectral radius of graphs with given degree sequences
Discrete Applied Mathematics
Erratum: Corrigendum: The extremal values of the Wiener index of a tree with given degree sequence
Discrete Applied Mathematics
Maxima and Minima of the Hosoya Index and the Merrifield-Simmons Index
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
On the number of independent subsets in trees with restricted degrees
Mathematical and Computer Modelling: An International Journal
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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.