Intersection Array
المؤلف:
Bendito, E.; Carmona, A.; and Encinas, A. M.
المصدر:
Shortest Paths in Distance-Regular Graphs." Europ. J. Combin. 21
الجزء والصفحة:
...
26-4-2022
1867
Intersection Array
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
![iota(gamma)=<span style=]() {b_0,b_1,...,b_(d-1);c_1,...,c_d} " src="https://mathworld.wolfram.com/images/equations/IntersectionArray/NumberedEquation1.svg" style="height:21px; width:236px" /> |
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 ![[[c_0,a_0,b_0],[c_1,a_1,b_1],[c_2,a_2,b_2],[c_3,a_3,b_3],[c_4,a_4,b_4]]](https://mathworld.wolfram.com/images/equations/IntersectionArray/Inline10.svg)
has intersection array ![<span style=]()
{b_0,b_1,b_2,b_3;c_1,c_2,c_3,c_4}" src="https://mathworld.wolfram.com/images/equations/IntersectionArray/Inline11.svg" style="height:24px; width:224px" />.
REFERENCES
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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