Merrifield-Simmons and Hosoya index of thorn-regular graphs
Authors: Boutiche M.A., Belbachir H., Gutman I.
Keywords: Merrifield-Simmons index; Hosoya index; thorn graph; independent vertex sets; independent edge sets
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.