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ON THE DEGREE DISTANCE OF SOME COMPOSITE GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  04 October 2011

HONGBO HUA
HONGBO HUA*
Affiliation:
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, Jiangsu 223003, PR China Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, Shaanxi 710072, PR China (email: [email protected])
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Abstract

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Let G be a connected simple graph. The degree distance of G is defined as D′(G)=∑ u∈V (G)dG(u)DG(u), where DG(u) is the sum of distances between the vertex u and all other vertices in G and dG(u) denotes the degree of vertex u in G. In contrast to many established results on extremal properties of degree distance, few results in the literature deal with the degree distance of composite graphs. Towards closing this gap, we study the degree distance of some composite graphs here. We present explicit formulas for D′ (G) of three composite graphs, namely, double graphs, extended double covers and edge copied graphs.

Keywords

degree distancedouble graphextended double coveredge copied graph

MSC classification

Secondary: 05C12: Distance in graphs 05C76: Graph operations (line graphs, products, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 1 , February 2012 , pp. 164 - 171
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

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