Distance-Regular Graphs with c i = b d-i and Antipodal Double Covers
Makoto Araya
and Akira Hiraki
DOI: 10.1023/A:1008681526048
Abstract
Let 
be a distance-regular graph of diameter d and valency k > 2. Suppose there exists an integer s with d 
2s such that c i = b d-i for all 1 i s. Then is an antipodal double cover.
be a distance-regular graph of diameter d and valency k > 2. Suppose there exists an integer s with d 2s such that c i = b d-i for all 1 i s. Then is an antipodal double cover.Pages: 127–138
Keywords: distance-regular graph; antipodal double cover; box; brox
Full Text: PDF
References
1. M. Araya, A. Hiraki and A. Juri\check sić, “Distance-regular graphs with bt = 1 and antipodal double-covers,” J. Combin. Th. (B) 67 (1996), 278-283.
2. M. Araya, A. Hiraki and A. Juri\check sić, “Distance-regular graphs with b2 = 1 and antipodal covers,” Europ. J. Combinatorics 18 (1997), 243-248.
3. E. Bannai and T. Ito, Algebraic Combinatorics I, Benjamin-Cummings, California, 1984.
4. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, Heidelberg, 1989.
5. A. Gardiner, “Antipodal covering graphs,” J. Combin. Th. (B) 16 (1974), 255-273.
2. M. Araya, A. Hiraki and A. Juri\check sić, “Distance-regular graphs with b2 = 1 and antipodal covers,” Europ. J. Combinatorics 18 (1997), 243-248.
3. E. Bannai and T. Ito, Algebraic Combinatorics I, Benjamin-Cummings, California, 1984.
4. A. E. Brouwer, A. M. Cohen, and A. Neumaier, Distance-Regular Graphs, Springer-Verlag, Berlin, Heidelberg, 1989.
5. A. Gardiner, “Antipodal covering graphs,” J. Combin. Th. (B) 16 (1974), 255-273.