Authors: Ilić, Aleksandar
Klavžar, Sandi
Stevanović, Dragan 
Title: Calculating the degree distance of partial Hamming graphs
Journal: Match
Volume: 63
Issue: 2
First page: 411
Last page: 424
Issue Date: 26-Apr-2010
Rank: M21a
ISSN: 0340-6253
Abstract: 
If G is a connected graph with vertex set V(G), then the degree distance of G is defined as DD{G) = Σ{u,v}∈V(G)(deg u + deg v)d{u,v), where deg u is the degree of vertex u, and d(u,v) denotes the distance between u and v. In the chemical Uterature, DD(G) is better known under the name Schultz index, introduced by Gutman. In the class of partial Hamming graphs, which include trees, benzenoid and phenylene systems among others, we express the degree distance in terms of the canonical metric representation, thus simplifying its computation.
Publisher: Faculty of Sciences, University of Kragujevac
Project: Serbian Ministry of Science, Research Grants 144007 and 144015G
Slovenian Agency for Research, Programs P1-0297 and P1-0285

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