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ArticleOriginal scientific text

Title

Wiener index of generalized stars and their quadratic line graphs

Authors 1, 1

Affiliations

  1. Sobolev Institute of Mathematics, Russian Academy of Sciences, Siberian Branch, Novosibirsk 630090, Russia

Abstract

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 Δ ≥ 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 ≤ Δ ≤ 6. Infinite families of generalized stars with this property are constructed.

Keywords

ENG
distance in a graph, Wiener index, star, iterated line graph

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Discussiones Mathematicae Graph Theory
2006/26/1
Export to PBN, Opens in new tab
Pages:
161-175
Main language of publication
English
Received
2005-06-24
Accepted
2005-07-22
Published
2006

DOI: 10.7151/dmgt.1310

Exact and natural sciences