Computing Eccentric Connectivity Polynomial of Fullerenes

Abstract

The eccentricity connectivity polynomial of a molecular graph G is defined as , where e(a) is defined as the length of a maximal path connecting a to other vertices of G. Fullerenes are 3-connected graphs with exactly 12 pentagonal faces. In this paper this polynomial is computed for an infinite family of fullerenes.

Keywords:

• Eccentricity connectivity polynomial
• eccentricity connectivity index
• fullerene graphs

Conclusion

Molecular descriptors play a prominent map in chemistry, pharmacology, and other disciplines. Among them, topological indices are very important. In this paper, by using a GAP program we compute the eccentric connectivity index of an infinite family of fullerenes.