Merrifield-Simmons and Hosoya index of thorn-regular graphs

Abstract

This paper deals with the Merrifield-Simmons and Hosoya indices of some thorn graphs. We outline a method for the calculation of these indices in the case of regular caterpillars and regular cyclic caterpillars. Then, by using a result of Belbachir & Bencherif, [Linear recurrent sequences and powers of a square matrix, Integers, Vol. 6, 2006, #A12], we obtain combinatorial expressions for these indices.

On Hosoya Index and Merrifield‐Simmons Index of trees with given domination number

“…By Lemma 2.3, Z(T 6 ) maximal and 𝜎(T 6 ) minimal in  n, n 2 . We use a similar technique used in Reference [21] for thorn-regular caterpillars to calculate values of T 6 . Obviously T 6 is a caterpillar graph…”