On Steiner degree distance of trees

Ivan Gutman

Applied Mathematics and Computation, 2016, vol. 283, issue C, 163-167

Abstract: Let G be a connected graph, and u, v, w its vertices. By du is denoted the degree of the vertex u, by d(u, v) the (ordinary) distance of the vertices u and v, and by d(u, v, w) the Steiner distance of u, v, w. The degree distance DD of G is defined as the sum of terms [du+dv]d(u,v) over all pairs of vertices of G. As early as in the 1990s, a linear relation was discovered between DD of trees and the Wiener index. We now consider SDD, the Steiner–distance generalization of DD, defined as the sum of terms [du+dv+dw]d(u,v,w) over all triples of vertices of G. Also in this case, a linear relation between SDD and the Wiener index could be established.

Keywords: Distance (in graph); Steiner distance; Degree distance; Wiener index (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:283:y:2016:i:c:p:163-167

DOI: 10.1016/j.amc.2016.02.038

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