We characterize the trees T with n vertices whose Hosoya index (total number of matchings) is Z(T ) > 16fn−5 resp. the trees whose Merrifield-Simmons index (total number of independent subsets) is σ(T ) < 18fn−5 + 21fn−6, where fk is the kth Fibonacci number. It turns out that all the trees satisfying the inequality are tripodes (trees with exactly three leaves) and the path in both cases. Furt...

In this study, we compute Merrifield-Simmons index of graphs which corresponds to PL (2, n) by using the decomposition formula. Examination shows that Merri-field-Simmons certain classes deduce as a result in difference equation. Further, prominent formula for and generating function are found number n hexagons state n). Also relations formed (PL n, n)) obtained combining two with angle between...

Abstract Many chemical indices have been invented in theoretical chemistry, such as Wiener index, Merrifield-Simmons index, Hosoya index, spectral radius and Randić index, etc. The extremal trees and unicyclic graphs for these chemical indices are interested in existing literature. Let G be a molecular graph (called a cacti), which all of blocks of G are either edges or cycles. Denote G (n, r) ...

We study the number of independent vertex subsets (known as the MerrifieldSimmons 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...

The Merrifield-Simmons index i G of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets of G The Hosoya index z G of a graph G is defined as the total number of independent edge subsets, that is, the total number of its matchings. By C n, k, λ we denote the set of graphs with n vertices, k cyc...