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
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

Show full item record


checked on Jun 15, 2024

Page view(s)

checked on May 9, 2024

Google ScholarTM




Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.