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Chang Graphs

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There are four strongly regular graphs with parameters (nu,k,lambda,mu)=(28,12,6,4), one of them being the triangular graph of order 8. The other three such graphs are known as the Chang graphs, illustrated above. The Chang graphs are also cospectral with the triangular graph T_8, all having graph spectrum (-2)^(20)4^712^1, meaning none of the these is determined by spectrum.

The Chang graphs are distance-regular with intersection array {12,5;1,4} but are not distance-transitive. They are pancyclic.

The Chang graphs are implemented in the Wolfram Language as GraphData[{"Chang", n}] for n=1, 2, 3.

See also

Determined by Spectrum, Paulus Graphs, Strongly Regular Graph, Triangular Graph

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References

Brouwer, A. E. "Chang Graphs." https://aeb.win.tue.nl/graphs/Chang.html.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. Distance-Regular Graphs. New York: Springer-Verlag, pp. 105-106, 1989.Brouwer, A. E. and van Lint, J. H. "Strongly Regular Graphs and Partial Geometries." In Enumeration and Design: Papers from the Conference on Combinatorics Held at the University of Waterloo, Waterloo, Ont., June 14-July 2, 1982 (Ed. D. M. Jackson and S. A. Vanstone). Toronto, Canada: Academic Press, pp. 85-122, 1984.Brualdi, R. and Ryser, H. J. Combinatorial Matrix Theory. New York: Cambridge University Press, p. 152, 1991.Chang, L.-C. "The Uniqueness and Non-Uniqueness of the Triangular Association Scheme." Sci. Record Peking Math. Soc. 3, 604-613, 1959.Chang, L.-C. "Association Schemes of Partially Balanced Designs with Parameters v=28, n_1=12, n_2=15, and p_(11)^2=4." Sci. Record Peking Math. 4, 12-18, 1960.DistanceRegular.org. "Chang Graphs (3 Graphs)." https://www.math.mun.ca/distanceregular/graphs/chang.html.Godsil, C. and Royle, G. Algebraic Graph Theory. New York: Springer-Verlag, p. 259, 2001.Hoffman, A. J. "On the Uniqueness of the Triangular Association Scheme." Ann. Math. Stat. 31, 492-497, 1960.House of Graphs. Chang Graphs. Chang Graph 1, Chang Graph 2, and Chang Graph 3.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

Chang Graphs

Cite this as:

Weisstein, Eric W. "Chang Graphs." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ChangGraphs.html

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