Wiener index of generalized 4-stars and of their quadratic line graphs
نویسندگان
چکیده
We construct several infinite families of trees which have a unique branching vertex of degree 4 and whose Wiener index equals the Wiener index of their quadratic line graph. This solves an open problem of Dobrynin and Mel’nikov.
منابع مشابه
Wiener index of generalized stars and their quadratic line graphs
The Wiener index, W , is the sum of distances between all pairs of vertices in a graph G. The quadratic line graph is defined as L(L(G)), where L(G) is the line graph of G. A generalized star S is a tree consisting of ∆ ≥ 3 paths with the unique common endvertex. A relation between the Wiener index of S and of its quadratic graph is presented. It is shown that generalized stars having the prope...
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 58 شماره
صفحات -
تاریخ انتشار 2014