Authors: Ilić, Aleksandar
Stevanović, Dragan 
Feng, Lihua
Yu, Guihai
Dankelmann, Peter
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Degree distance of unicyclic and bicyclic graphs
Journal: Discrete Applied Mathematics
Volume: 159
Issue: 8
First page: 779
Last page: 788
Issue Date: 28-Apr-2011
Rank: M22
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.01.013
Abstract: 
Let G be a connected graph with vertex set V(G). The degree distance of G is defined as D′(G)=∑u,v⊆V(G)(degG(u)+degG(v))d(u,v), where degG(u) is the degree of vertex u, and d(u,v) denotes the distance between u and v. Here we characterize n-vertex unicyclic graphs with girth k, having minimum and maximum degree distance, respectively. Furthermore, we prove that the graph Bn, obtained from two triangles linked by a path, is the unique graph having the maximum degree distance among bicyclic graphs, which resolves a recent conjecture of Tomescu.
Keywords: Bicyclic graph | Degree distance | Girth | Wiener index
Publisher: Elsevier
Project: NNSFC (Nos. 70901048, 10871205)
NSFSD (Nos. BS2010SF017, Y2008A04)
Serbian Ministry of Science, Project 144007 and 144015G
Slovenian Agency for Research, Program P1-0285

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