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Ivanov-Ivanov-Faradjev Graph

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The Ivanov-Ivanov-Faradjev graph is a distance-regular graph on 990 vertices (Brouwer et al. 1989, p. 369). It has intersection array {7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7} and is also distance-transitive.

It is a weakly regular graph of order 7, and has graph spectrum

(-4)^(21)(-1/2(1+sqrt(33)))^(154)(-3)^(99)0^(198)1^(154)×(1/2(-1+sqrt(33)))^(154)4^(55)5^(42)7^1

(van Dam and Haemers 2003).

The Ivanov-Ivanov-Faradjev graph is implemented in the Wolfram Language as GraphData["IvanovIvanovFaradjevGraph"].

See also

Cubic Semisymmetric Graph, Doubly Truncated Witt Graph, Iofinova-Ivanov Graphs, Large Witt Graph, Ljubljana Graph, Semisymmetric Graph, Truncated Witt Graph, Witt Design

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References

Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. "The Ivanov-Ivanov-Faradjev Graph." §11.4D in Distance Regular Graphs. New York: Springer-Verlag, pp. 369-370, 1989.DistanceRegular.org. "Ivanov-Ivanov-Faradjev Graph." http://www.distanceregular.org/graphs/iif.html.Faradjev, I. A.; Ivanov, A. A.; and Ivanov, A. V. "Distance-Transitive Graphs of Valency 5, 6 and 7." Europ. J. Combin. 7, 303-319, 1986.van Dam, E. R. and Haemers, W. H. "Which Graphs Are Determined by Their Spectrum?" Lin. Algebra Appl. 373, 139-162, 2003.

Referenced on Wolfram|Alpha

Ivanov-Ivanov-Faradjev Graph

Cite this as:

Weisstein, Eric W. "Ivanov-Ivanov-Faradjev Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ivanov-Ivanov-FaradjevGraph.html

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