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.
Original language | English |
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Pages (from-to) | 779-788 |
Number of pages | 10 |
Journal | Discrete Applied Mathematics |
Volume | 159 |
Issue number | 8 |
DOIs | |
Publication status | Published - 28 Apr 2011 |
Externally published | Yes |
Keywords
- Bicyclic graph
- Degree distance
- Girth
- Wiener index
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics