|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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