Extremal Graphs under Wiener–type Invariants

چکیده مقاله

Letd(G, k) be the number of pairs of vertices of a graph Gthat are at distancek, λarealnumber,andWλ(G)= k≥1 d(G, k)k λ . Wλ(G) is called the Wiener-type invariant ofGassociated to real numberλ. In this paper, the Wienertype invariant of the Cartesian product of graphs is computed. As an application the Tratch−Stankevich−Zefirov ofC4 nanotubes and nanotori are computed. We also find some new bound for this graph invariant.