A Distance-Regular Graph with Strongly Closed Subgraphs
Akira Hiraki
DOI: 10.1023/A:1011933828085
Abstract
Let 
be a distance-regular graph of diameter d, valency k and r := max i | ( c i, b i) = ( c 1, b 1). Let q be an integer with r + 1 
q d - 1.
be a distance-regular graph of diameter d, valency k and r := max i | ( c i, b i) = ( c 1, b 1). Let q be an integer with r + 1 q d - 1. In this paper we prove the following results:
Pages: 127–131
Keywords: distance-regular graph; strongly closed subgraph
Full Text: PDF
References
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7. A. Hiraki, “Distance-regular subgraphs in a distance-regular graph, VI,” Europ. J. Combin. 19 (1998), 953- 965.
8. A. Hiraki, “Strongly closed subgraphs in a regular thick near polygon,” Europ. J. Combin. 20 (1999), 789-796.
9. A. Hiraki, “A characterization of the doubled Grassmann graphs, the doubled Odd graphs, and the Odd graphs by strongly closed subgraphs,” preprint.
10. A. Hiraki and J. Koolen, “An improvement of the Ivanov bound,” Ann. Combin. 2 (1998), 131-135.
11. A. Hiraki and J. Koolen, “An improvement of the Godsil bound,” To appear in Ann. Combin.
12. H. Suzuki, “On strongly closed subgraphs of highly regular graphs,” Europ. J. Combin. 16 (1995), 197-220.
2. A.E. Brouwer, A.M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer Verlag, Berlin, Heidelberg, 1989.
3. Y.L. Chen and A. Hiraki, “On the non-existence of certain distance-regular graphs,” Kyushu J. Math. 53 (1999), 1-15.
4. A. Hiraki, “An improvement of the Boshier-Nomura bound, J. Comb. Theory Ser. B 61 (1994), 1-4.
5. A. Hiraki, “Distance-regular subgraphs in a distance-regular graph, I-II,” Europ. J. Combin. 16 (1995), 589- 602, 603-615.
6. A. Hiraki, “Distance-regular subgraphs in a distance-regular graph, V,” Europ. J. Combin. 19 (1998), 141-150.
7. A. Hiraki, “Distance-regular subgraphs in a distance-regular graph, VI,” Europ. J. Combin. 19 (1998), 953- 965.
8. A. Hiraki, “Strongly closed subgraphs in a regular thick near polygon,” Europ. J. Combin. 20 (1999), 789-796.
9. A. Hiraki, “A characterization of the doubled Grassmann graphs, the doubled Odd graphs, and the Odd graphs by strongly closed subgraphs,” preprint.
10. A. Hiraki and J. Koolen, “An improvement of the Ivanov bound,” Ann. Combin. 2 (1998), 131-135.
11. A. Hiraki and J. Koolen, “An improvement of the Godsil bound,” To appear in Ann. Combin.
12. H. Suzuki, “On strongly closed subgraphs of highly regular graphs,” Europ. J. Combin. 16 (1995), 197-220.
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