Dejter Graph

The Dejter graph is a weakly regular graph on 112 vertices and 336 edges with regular paremeters (nu,k,lambda,mu)=(112,6,0,(0,1,2)). It can be obtained by deleting a copy of the length-7 Hamming code from the hypercube graph Q_7 constructed as a binary 7-cube. It is also related to the Ljubljana graph.

The Dejter graph is bipartite.

It is implemented in the Wolfram Language as GraphData["DejterGraph"].

See also

Hypercube Graph, Ljubljana Graph, Weakly Regular Graph

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Borges, J. and Dejter, I. J. "On Perfect Dominating Sets in Hypercubes and Their Complements." J. Combin. Math. Combin. Comput. 20, 161-173, 1996.Dejter, I. J. "On Symmetric Subgraphs of the 7-Cube: an Overview." Disc. Math. 124, 55-66, 1994.Dejter, I. J. "Symmetry of Factors of the 7-Cube Hamming Shell." J. Combin. Des. 5, 301-309, 1997.Dejter, I. J. and Guan P. "Square-Blocking Edge Subsets in Hypercubes and Vertex Avoidance." In Graph Theory, Combinatorics, Algorithms, and Applications (San Francisco, CA, 1989). Philadelphia, PA: SIAM, pp. 162-174, 1991.Dejter, I. J. and Pujol, J. "Perfect Domination and Symmetry in Hypercubes." In Proceedings of the Twenty-sixth Southeastern International Conference on Combinatorics, Graph Theory and Computing (Boca Raton, Florida, 1995). Congr. Numer. 111, 18-32, 1995.Dejter, I. J. and Weichsel P. M. "Twisted Perfect Dominating Subgraphs of Hypercubes." In Proceedings of the Twenty-Fourth Southeastern International Conference on Combinatorics, Graph Theory, and Computing (Boca Raton, Florida, 1993). Congr. Numer. 94, 67-78, 1993.Klin, M.; Lauri, J.; and Ziv-Av, M. "Links Between Two Semisymmetric Graphs on 112 Vertices Via Association Schemes." J. Symb. Comput. 47, 1175-1191, 2012.

Cite this as:

Weisstein, Eric W. "Dejter Graph." From MathWorld--A Wolfram Web Resource.

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