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.
KeywordsAdjacency Matrix Connected Graph Spectral Radius Regular Graph Line Graph
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References and Further Reading
- 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.A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Classics in Applied Mathematics, 9, SIAM, Philadelphia, 1994.Google Scholar
- 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