The Merrifield–Simmons Index of the Fullerene Derivative Hexagonal System

Abstract

The fullerene derivative hexagonal system is obtained from fullerene C_n and hexagonal system sticked by a common edge. The Merrifield–Simmons index of a graph G is defined as the total number of the independent sets of G. In this paper, we give the lower and larger bound of Merrifield–Simmons index of the fullerene derivative hexagonal system. Furthermore, we give two formulas of the Merrifield–Simmons index of the fullerene derivative hexagonal system C₂₀ ⊗ l(n) and C₂₀ ⊗ (l(n₁), l(n₂)).

Keywords:

• Fullerene
• Fullerene derivative
• Hexagonal system
• Merrifield–Simmons index

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by NSFC (11761056), Education Department of Shaanxi Province (15JK1143, 18JK0162).