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The graph Q 0 consists of a single vertex, while Q 1 is the complete graph on two vertices. Q 2 is a cycle of length 4. The graph Q 3 is the 1-skeleton of a cube and is a planar graph with eight vertices and twelve edges. The graph Q 4 is the Levi graph of the Möbius configuration. It is also the knight's graph for a toroidal chessboard.
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.
Here is an angle in the unit circle; taking 1 / 3 of that angle corresponds to taking a cube root of a complex number; adding −k 2 π / 3 for k = 1, 2 finds the other cube roots; and multiplying the cosines of these resulting angles by corrects for scale.
The graph of any cubic function is similar to such a curve. The graph of a cubic function is a cubic curve, though many cubic curves are not graphs of functions. Although cubic functions depend on four parameters, their graph can have only very few shapes. In fact, the graph of a cubic function is always similar to the graph of a function of ...
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 ...
3. Folded cube graph, formed from a hypercube by adding a matching connecting opposite vertices. 4. Halved cube graph, the half-square of a hypercube graph. 5. Partial cube, a distance-preserving subgraph of a hypercube. 6. The cube of a graph G is the graph power G 3. 7. Cubic graph, another name for a 3-regular graph, one in which each vertex ...
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A fan of order n is defined to be a graph on the vertices {0, 1, ..., n} with 2n − 1 edges connected according to the following rules: Vertex 0 is connected by a single edge to each of the other n vertices, and vertex is connected by a single edge to the next vertex k + 1 for all 1 ≤ k < n. [24]