Symmetry-Moderated Wiener Index

چکیده مقاله

The modified Wiener index is an algebraic modification of the classical Wiener index under symmetry group. This graph invariant was presented by Graovac and Pisanski in 1991. In this paper, the modified Wiener polynomial Ŵ(G,x) of a graph G is presented by which we extend some well-known results of the classical Wiener index to its modified version. Moreover, the modified Wiener polynomials of some classes of chemical graphs containing linear phenylene and its hexagonal squeeze, and the ortho-, meta- and para-polyphenylene chains are computed .