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Table of simple cubic graphs : ウィキペディア英語版 | Table of simple cubic graphs The connected 3-regular (cubic) simple graphs are listed for small vertex numbers. ==Connectivity== The number of simple cubic graphs on 4, 6, 8, 10,... vertices is 1, 2, 5, 19,... . A classification according to edge connectivity is made as follows: the 1-connected and 2-connected graphs are defined as usual. This leaves the other graphs in the 3-connected class because each 3-regular graph can be split by cutting all edges adjacent to any of the vertices. To refine this definition in the light of the algebra of coupling of angular momenta (see below), a subdivision of the 3-connected graphs is helpful. We shall call * Non-trivially 3-connected those that can be split by 3 edge cuts into sub-graphs with at least two vertices remaining in each part * Cyclically 4-connected—all those not 1-connected, not 2-connected, and not non-trivially 3-connected This declares the numbers 3 and 4 in the fourth column of the tables below.
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