Original scientific paper

Trees, Quadratic Line Graphs and the Wiener Index

Andrey A. Dobrynin orcid.org/0000-0003-0074-8388 ; Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630 090, Russia
Leonid S. Mel'nikov ; Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630 090, Russia

Abstract

The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a tree. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most (chemical trees). The line graph L(G) of a graph G has the vertex set V(L(G)) = E(G) and two distinct vertices of L(G) are adjacent if the corresponding edges of G have a common endvertex. It is known that the Wiener indices of a tree and of its line graph are always distinct. An infinite two-parameter family of growing chemical trees T with the property W(T) = W(L(L(T))) has been constructed.

Keywords

topological index; Wiener index; tree; line graph

Hrčak ID:

102948

URI

https://hrcak.srce.hr/102948

Publication date:

25.10.2004.

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