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Date: 6-8-2016
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Date: 29-4-2022
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Given a distance-regular graph with integers
such that for any two vertices
at distance
, there are exactly
neighbors of
and
neighbors of
, the sequence
is called the intersection array of .
A similar type of intersection array can also be defined for a distance-transitive graph.
A distance-regular graph with global parameters has intersection array
.
Bendito, E.; Carmona, A.; and Encinas, A. M. "Shortest Paths in Distance-Regular Graphs." Europ. J. Combin. 21, 153-166, 2000.
Biggs, N. L. Algebraic Graph Theory, 2nd ed. Cambridge, England: Cambridge University Press, 1993.
Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, 1989.
Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, p. 68, 2001.
van Dam, E. R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.
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