![]() on Parallel Processing, vol. 1, Silver Spring, MD: IEEE Computer Society Press, pp. 103–110. (1989), "On the Permutation Capability of a Circuit-Switched Hypercube", Proc. (2000), "On the Achromatic Number of Hypercubes", Journal of Combinatorial Theory, Series B, 79 (2): 177–182, doi: 10.1006/jctb.2000.1955. A hypercube in 4 dimensions has 16 vertices, 32 edges, 24 square faces, and 8 cubic hyperfaces which form its boundary. ^ Optimal Numberings and Isoperimetric Problems on Graphs, L.H. ![]() (1955), "Über drei kombinatorische Probleme am n-dimensionalen Wiirfel und Wiirfelgitter", Abh. Matchings extend to Hamiltonian cycles in hypercubes on Open Problem Garden. P of G in H is the proportion of the total number of vertices (resp. (2007), "Perfect matchings extend to Hamiltonian cycles in hypercubes", Journal of Combinatorial Theory, Series B, 97 (6): 1074–1076, doi: 10.1016/j.jctb.2007.02.007. For a graph G (V,E), a binary vertex labeling (coloring) f : V (G) Z2, is said to be friendly if the number of vertices labeled 0 is almost. We show that deleting k - 2 vertices and/or edges cannot increase the diameter, deleting k - 1 can increase it by at most 1, and the sets of size k - 1 that increase it by 1 are the sets obtained from local cuts by deleting one element. Some further results on C 4-avoiding sets of edges which are connecting vertices of three consecutive levels of the hypercube can be found in 11. The hypercube is far from this extreme in some sense, Q k is a very highly interconnected k -connected graph. Hypercube graph represents the maximum number of edges that can be connected to a graph to make it an n degree graph, every vertex has the same degree n and in that representation, only a fixed number of edges and vertices are added as shown in the figure below: All hypercube graphs are Hamiltonian, hypercube graph of order n has (2n) vertices. (1963), "Some complete cycles on the n-cube", Proceedings of the American Mathematical Society, American Mathematical Society, 14 (4): 640–643, doi: 10.2307/2034292, JSTOR 2034292. For small values of n, the exact number of edges in a largest C 4-free subgraph of Q n was determined in 7, 10. (2004), Across the Board: The Mathematics of Chessboard Problems, Princeton University Press, p. 68, ISBN 978-8-5. The family Q n for all n > 1 is a Lévy family of graphs Problems
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