Resistance Distance

Part of the Universitext book series (UTX)

Let G be a connected graph with V(G) = {1,⋯,n}. The shortest path distance d(i, j) between the vertices i, j 2 V(G) is the classical notion of distance and is extensively studied. However, this concept of distance is not always appropriate. Consider the following two graphs


Random Walk Span Tree Connected Graph Minimum Norm Classical Distance 
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References and Further Reading

  1. 1.
    R.B. Bapat, Resistance distance in graphs, The Mathematics Student, 68:87–98 (1999).MathSciNetGoogle Scholar
  2. 2.
    R.B. Bapat, Resistance matrix of a weighted graph, MATCH Communications in Mathematical and in Computer Chemistry, 50:73–82 (2004).MathSciNetzbMATHGoogle Scholar
  3. 3.
    B. Bollobás, Modern Graph Theory, Springer-Verlag, New York, 1998.zbMATHGoogle Scholar
  4. 4.
    P.G. Doyle and J.L. Snell, Random Walks and Electrical Networks, Math. Assoc. Am., Washington, 1984.Google Scholar
  5. 5.
    D.J. Klein and M. Randić, Resistance distance, Journal of Mathematical Chemistry, 12:81–95 (1993).CrossRefMathSciNetGoogle Scholar

Copyright information

© Hindustan Book Agency (India) 2010

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