Tree-like polyphenyl systems with extremal Wiener indices ∗

The Wiener index of a connected graph is the sum of the distances between all pairs of vertices of the graph. In this paper, we determine the polyphenyl chains with minimum and maximum Wiener indices among all the polyphenyl chains with h hexagons, and the tree-like polyphenyl system with maximum Wiener index. Moreover, explicit formulas for the Wiener indices of extremal polyphenyl chains are obtained.