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  • ON THE DEGREE DISTANCE OF SOME COMPOSITE GRAPHS

  • Part of
  • HONGBO HUA
  • Journal:
    Bulletin of the Australian Mathematical Society / Volume 85 / Issue 1 / February 2012
    Published online by Cambridge University Press:
    04 October 2011, pp. 164-171
    Print publication:
    February 2012
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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.