When.com Web Search

Search results

  1. Results From The WOW.Com Content Network
  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

    The number of connected simple cubic graphs on 4, 6, 8, 10, ... vertices is 1, 2, 5, 19, ... (sequence A002851 in the OEIS). 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 ...

  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. 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.

  6. Cube-connected cycles - Wikipedia

    en.wikipedia.org/wiki/Cube-connected_cycles

    The cube-connected cycles of order n (denoted CCC n) can be defined as a graph formed from a set of n2 n nodes, indexed by pairs of numbers (x, y) where 0 ≤ x < 2 n and 0 ≤ y < n. Each such node is connected to three neighbors: ( x , ( y + 1) mod n ) , ( x , ( y − 1) mod n ) , and ( x ⊕ 2 y , y ) , where "⊕" denotes the bitwise ...

  7. Regular graph - Wikipedia

    en.wikipedia.org/wiki/Regular_graph

    Regular graphs of degree at most 2 are easy to classify: a 0-regular graph consists of disconnected vertices, a 1-regular graph consists of disconnected edges, and a 2-regular graph consists of a disjoint union of cycles and infinite chains. A 3-regular graph is known as a cubic graph.

  8. Cube - Wikipedia

    en.wikipedia.org/wiki/Cube

    It is also a 3-connected graph, meaning that, whenever a graph with more than three vertices, and two of the vertices are removed, the edges remain connected. [27] [28] The skeleton of a cube can be represented as the graph, and it is called the cubical graph, a Platonic graph. It has the same number of vertices and edges as the cube, twelve ...

  9. 9-cube - Wikipedia

    en.wikipedia.org/wiki/9-cube

    This 9-cube graph is an orthogonal projection. This orientation shows columns of vertices positioned a vertex-edge-vertex distance from one vertex on the left to one vertex on the right, and edges attaching adjacent columns of vertices. The number of vertices in each column represents rows in Pascal's triangle, being 1:9:36:84:126:126:84:36:9:1.