Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4625683 | Applied Mathematics and Computation | 2016 | 6 Pages |
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)W=∑{u,v}⊆V(G)d(u,v). We examine the difference DD−ZZDD−ZZ for trees and establish a number of regularities.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Ivan Gutman, Boris Furtula, Kinkar Ch. Das,