On some degree-and-distance-based graph invariants of trees

Ivan Gutman, Boris Furtula and Kinkar Ch. Das

Applied Mathematics and Computation, 2016, vol. 289, issue C, 1-6

Abstract: Let G be a connected graph with vertex set V(G). For u, v ∈ V(G), d(v) and d(u, v) denote the degree of the vertex v and the distance between the vertices u and v. A much studied degree–and–distance–based graph invariant is the degree distance, defined as DD=∑{u,v}⊆V(G)[d(u)+d(v)]d(u,v). A related such invariant (usually called “Gutman index”) is ZZ=∑{u,v}⊆V(G)[d(u)·d(v)]d(u,v). If G is a tree, then both DD and ZZ are linearly related with the Wiener index W=∑{u,v}⊆V(G)d(u,v). We examine the difference DD−ZZ for trees and establish a number of regularities.

Keywords: Distance (in graph); Degree distance; Wiener index; Gutman index (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:289:y:2016:i:c:p:1-6

DOI: 10.1016/j.amc.2016.04.040

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