The 
-Ustimenko
graph is the distance-1 or distance-2 graph of the dual polar graph on ![[C_m(q)]](/images/equations/UstimenkoGraph/Inline2.svg)
(Brouwer et al. 1989, p. 279). The Ustimenko
graph with parameters 
and 
is distance-regular with regular parameters
![(d,q^2,[3; 1]_q-1,[m+1; 1]_q-1)](/images/equations/UstimenkoGraph/Inline5.svg)
, where
![[n; k]_q](/images/equations/UstimenkoGraph/Inline6.svg)
is a q-binomial
coefficient.
Ustimenko Graph
See also
Distance-Regular GraphExplore with Wolfram|Alpha
References
Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, p. 279, 1989.Ivanov, A. A.; Muzichuk, M. E.; and Ustimenko, V. A., "On a New Family of (
and 
)-Polynomial
Schemes." European J. Combin. 10, 337-345, 1989.
van Dam, E. R.; Koolen, J. H.; and Tanaka, H. "Distance-Regular Graphs."
Elec. J. Combin. No. DS 22, p. 22, Apr. 2016. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS22.
Cite this as:
Weisstein, Eric W. "Ustimenko Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/UstimenkoGraph.html