Wiener index versus maximum degree in trees
Discrete Applied Mathematics
Maximizing the number of independent subsets over trees with bounded degree
Journal of Graph Theory
Largest Number of Subtrees of Trees with a Given Maximum Degree
SIAM Journal on Discrete Mathematics
Note: On extremal unicyclic molecular graphs with maximal Hosoya index
Discrete Applied Mathematics
Note: Fibonacci numbers and Lucas numbers in graphs
Discrete Applied Mathematics
The number of independent sets in unicyclic graphs
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
The smallest Merrifield-Simmons index of (n,n+1)-graphs
Mathematical and Computer Modelling: An International Journal
Minimizing a class of unicyclic graphs by means of Hosoya index
Mathematical and Computer Modelling: An International Journal
Energy, Hosoya index and Merrifield-Simmons index of trees with prescribed degree sequence
Discrete Applied Mathematics
| Hi-index | 0.98 |
We study the number of independent vertex subsets (known as the Merrifield-Simmons index in mathematical chemistry) and the number of independent edge subsets (called the Hosoya index) for trees whose vertex degrees are restricted to 1 or d (for some d=3), a natural restriction in the chemical context. We find that the minimum of the Merrifield-Simmons index and the maximum of the Hosoya index are both attained for path-like trees; furthermore, one obtains the second-smallest value of the Merrifield-Simmons index and the second-largest value of the Hosoya index for generalized tripods. Analogous results are also found for a closely related parameter, the graph energy, which also plays an important role in mathematical chemistry.