Original scientific paper

A New Hyper-Wiener Index

Ivan Gutman ; Faculty of Science, University of Kragujevac, 34000 Kragujevac, Serbia and Montenegro

Abstract

If two edges e and f are deleted from a tree T, then it decomposes into three components, possessing, n₀(e, f ), n₁(e, f ), and n₂(e, f ) vertices. Let n₀(e, f ) count the vertices lying between the edges e and f. It is shown that the Wiener index W of the tree T is equal to the sum over all edges e of the products n₁(e, e) • n₂(e, e), and that the hyper-Wiener index WW of T is the sum over all pairs of edges e, f of the products n₁(e, f ) • n₂(e, f ). We now consider another structure-descriptor, denoted by WWW, equal to the sum over all pairs of edges of the products n0(e, f ) • n₁(e, f ) • n₂(e, f ). We establish some basic properties of WWW and show how it is related to W.

Keywords

Wiener index, W; hyper-Wiener index, WW; WWW index

Hrčak ID:

102646

URI

https://hrcak.srce.hr/102646

Publication date:

31.5.2004.

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