A Characterization of Distance-Regular Graphs with Diameter Three
Edwin R. van Dam
and Willem H. Haemers
DOI: 10.1023/A:1008626416743
Abstract
We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.
Pages: 299–303
Keywords: distance-regular graph; eigenvalues of graphs
Full Text: PDF
References
1. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-regular graphs, Ergebnisse der Mathematik 3.18, Springer, Heidelberg, 1989.
2. E.R. van Dam, “Regular graphs with four eigenvalues,” Linear Algebra Appl. 226-228 (1995), 139-162.
3. E.R. van Dam, “Bounds on special subsets in graphs, eigenvalues and association schemes,” J. Alg. Combin. (to appear).
4. E.R. van Dam, “Graphs with few eigenvalues-An interplay between combinatorics and algebra,” Thesis, Tilburg University, Center dissertation series 20, 1996.
5. W.H. Haemers, “Interlacing eigenvalues and graphs,” Linear Algebra Appl. 226-228 (1995), 593-616.
6. W.H. Haemers, “Distance-regularity and the spectrum of graphs,” Linear Algebra Appl. 236 (1996), 265-278.
7. A.J. Hoffman, “On the polynomial of a graph,” Amer. Math. Monthly 70 (1963), 30-36.
2. E.R. van Dam, “Regular graphs with four eigenvalues,” Linear Algebra Appl. 226-228 (1995), 139-162.
3. E.R. van Dam, “Bounds on special subsets in graphs, eigenvalues and association schemes,” J. Alg. Combin. (to appear).
4. E.R. van Dam, “Graphs with few eigenvalues-An interplay between combinatorics and algebra,” Thesis, Tilburg University, Center dissertation series 20, 1996.
5. W.H. Haemers, “Interlacing eigenvalues and graphs,” Linear Algebra Appl. 226-228 (1995), 593-616.
6. W.H. Haemers, “Distance-regularity and the spectrum of graphs,” Linear Algebra Appl. 236 (1996), 265-278.
7. A.J. Hoffman, “On the polynomial of a graph,” Amer. Math. Monthly 70 (1963), 30-36.