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  2. Cubic graph - Wikipedia

    en.wikipedia.org/wiki/Cubic_graph

    According to Brooks' theorem every connected cubic graph other than the complete graph K 4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K 4 has an independent set of at least n/3 vertices, where n is the number of vertices in the graph: for instance, the largest color class in a 3-coloring has at least this many vertices.

  3. Table of simple cubic graphs - Wikipedia

    en.wikipedia.org/wiki/Table_of_simple_cubic_graphs

    Roughly speaking, each vertex represents a 3-jm symbol, the graph is converted to a digraph by assigning signs to the angular momentum quantum numbers j, the vertices are labelled with a handedness representing the order of the three j (of the three edges) in the 3-jm symbol, and the graph represents a sum over the product of all these numbers ...

  4. Möbius ladder - Wikipedia

    en.wikipedia.org/wiki/Möbius_ladder

    In graph theory, the Möbius ladder M n, for even numbers n, is formed from an n-cycle by adding edges (called "rungs") connecting opposite pairs of vertices in the cycle. It is a cubic, circulant graph, so-named because (with the exception of M 6 (the utility graph K 3,3), M n has exactly n/2 four-cycles [1] which link together by their shared edges to form a topological Möbius strip.

  5. Cubic function - Wikipedia

    en.wikipedia.org/wiki/Cubic_function

    The points P 1, P 2, and P 3 (in blue) are collinear and belong to the graph of x 3 + ⁠ 3 / 2 ⁠ x 2 − ⁠ 5 / 2 ⁠ x + ⁠ 5 / 4 ⁠. The points T 1, T 2, and T 3 (in red) are the intersections of the (dotted) tangent lines to the graph at these points with the graph itself. They are collinear too.

  6. Template:Cubic graph special points.svg - Wikipedia

    en.wikipedia.org/wiki/Template:Cubic_graph...

    This page was last edited on 4 February 2024, at 16:35 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.

  7. Balaban 10-cage - Wikipedia

    en.wikipedia.org/wiki/Balaban_10-cage

    There exist 3 distinct (3,10)-cages, the other two being the Harries graph and the Harries–Wong graph. [5] Moreover, the Harries–Wong graph and Harries graph are cospectral graphs. The Balaban 10-cage has chromatic number 2, chromatic index 3, diameter 6, girth 10 and is hamiltonian. It is also a 3-vertex-connected graph and 3-edge-connected.

  8. Gray graph - Wikipedia

    en.wikipedia.org/wiki/Gray_graph

    In the mathematical field of graph theory, the Gray graph is an undirected bipartite graph with 54 vertices and 81 edges. It is a cubic graph : every vertex touches exactly three edges. It was discovered by Marion C. Gray in 1932 (unpublished), then discovered independently by Bouwer 1968 in reply to a question posed by Jon Folkman 1967.

  9. Crossing number (graph theory) - Wikipedia

    en.wikipedia.org/wiki/Crossing_number_(graph_theory)

    The smallest cubic graphs with crossing numbers 1–11 are known (sequence A110507 in the OEIS). The smallest 1-crossing cubic graph is the complete bipartite graph K 3,3, with 6 vertices. The smallest 2-crossing cubic graph is the Petersen graph, with 10 vertices. The smallest 3-crossing cubic graph is the Heawood graph, with 14 vertices