Regular Graphs

Part of the Universitext book series (UTX)

A graph is said to be regular if all its vertices have the same degree. If the degree of each vertex of G is k, then G is said to be k-regular. Examples of regular graphs include cycles, complete graphs and complete bipartite graphs with bipartite sets of the same cardinality.


Adjacency Matrix Connected Graph Spectral Radius Regular Graph Line Graph 
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References and Further Reading

  1. 1.
    R.B. Bapat and T.E.S. Raghavan, Nonnegative Matrices and Applications, Encyclopedia of Mathematics and Its Applications, 64, Cambridge University Press, Cambridge, 1997.Google Scholar
  2. 2.
    A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, 9, SIAM, Philadelphia, 1994.Google Scholar
  3. 3.
    P. J. Cameron, Strongly regular graphs, In Selected Topics in Graph Theory L.W. Beineke and R.J. Wilson, Ed. Academic Press, New York, pp. 337–360 (1978).Google Scholar
  4. 4.
    C.D. Godsil, Algebraic Combinatorics, Chapman and Hall, Inc., New York, 1993.zbMATHGoogle Scholar
  5. 5.
    J. H. Koolen and V. Moulton, Maximal energy graphs, Advances in Applied Mathematics, 26:47–52 (2001).CrossRefMathSciNetzbMATHGoogle Scholar

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