Wiener index of generalized stars and their quadratic line graphs | Zendy

Andrey A. Dobrynin | Zendy; Leonid S. Mel’nikov | Zendy

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Wiener index of generalized stars and their quadratic line graphs

Author(s) -

Andrey A. Dobrynin,

Leonid S. Mel’nikov

Publication year - 2006

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.1310

Subject(s) - wiener index , mathematics , combinatorics , quadratic equation , line graph , graph , stars , discrete mathematics , physics , geometry , astrophysics

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 property W (S) = W (L(L(S)) exist only for 4 ≤ ∆ ≤ 6. Infinite families of generalized stars with this property are constructed.

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