释义 |
Superregular GraphFor a Vertex of a Graph, let and denote the Subgraphs of induced by the Vertices adjacent to andnonadjacent to , respectively. The empty graph is defined to be superregular, and is said to be superregularif is a Regular Graph and both and are superregular for all .
The superregular graphs are precisely , ( ), ( ), and the complements of these graphs,where is a Cyclic Graph, is a Complete Graph and is disjoint copies of , and is the Cartesian product of with itself (the graph whose Vertex set consists of Vertices arranged in an square with two Vertices adjacentIff they are in the same row or column). See also Complete Graph, Cyclic Graph, Regular Graph References
Vince, A. ``The Superregular Graph.'' Problem 6617. Amer. Math. Monthly 103, 600-603, 1996.West, D. B. ``The Superregular Graphs.'' J. Graph Th. 23, 289-295, 1996.
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