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# 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

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 .

Distance-Regular Graph, Distance-Transitive Graph, Global Parameters

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## 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.Koolen, J. H.; Yu, K.; Liang, X.; Choi, H.; and Markowsky, G. "Non-Geometric Distance-Regular Graphs of Diameter at Least 3 With Smallest Eigenvalue at Least ." 15 Nov 2023. https://arxiv.org/abs/2311.09001.van Dam, E. R. and Haemers, W. H. "Spectral Characterizations of Some Distance-Regular Graphs." J. Algebraic Combin. 15, 189-202, 2003.

## Referenced on Wolfram|Alpha

Intersection Array

## Cite this as:

Weisstein, Eric W. "Intersection Array." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IntersectionArray.html