𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The maximum Wiener polarity index of trees with pendants

✍ Scribed by Hanyuan Deng; Hui Xiao

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
327 KB
Volume
23
Category
Article
ISSN
0893-9659

No coin nor oath required. For personal study only.

✦ Synopsis

The Wiener polarity index W p (G) of a graph G = (V , E) is the number of unordered pairs of vertices {u, v} of G such that the distance d G (u, v) between u and v is 3. In this work, we give the maximum Wiener polarity index of trees with n vertices and k pendants and find that the maximum value is independent of k when k + 2 ≀ n ≀ 2k. The corresponding extremal trees are characterized.

πŸ“œ SIMILAR VOLUMES

Determination of the Wiener molecular br
Determination of the Wiener molecular branching index for the general tree
✍ E. R. Canfield; R. W. Robinson; D. H. Rouvray πŸ“‚ Article πŸ“… 1985 πŸ› John Wiley and Sons 🌐 English βš– 928 KB

The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the for

On graphs with the maximum number of spa
On graphs with the maximum number of spanning trees
✍ Alexander K. Kelmans πŸ“‚ Article πŸ“… 1996 πŸ› John Wiley and Sons 🌐 English βš– 814 KB

Let 3:; denote the set of simple graphs with n vertices and m edges, t ( G ) the number of spanning trees of a graph G , and F 2 H if t(K,\E(F))?t(K,\E(H)) for every s? max{u(F), u ( H ) } . We give a complete characterization of >-maximal (maximum) graphs in 3:; subject to m 5 n . This result conta