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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 ...
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.
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.
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.
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 It was discovered by Marion C. Gray in 1932 (unpublished), then discovered independently by Bouwer 1968 in reply to a question posed by Jon Folkman 1967.
Tetrahedral graph – 4 vertices, 6 edges; Octahedral graph – 6 vertices, 12 edges; Cubical graph – 8 vertices, 12 edges; Icosahedral graph – 12 vertices, 30 edges; Dodecahedral graph – 20 vertices, 30 edges; A polyhedral graph is the graph of a simple polyhedron if it is cubic (every vertex has three edges), and it is the graph of a ...
3 for n=3 5 for n=5 6 for n≥7: Chromatic number: 3: Chromatic index: 4: Book thickness: ... the Flower snark J n is a cubic graph with 4n vertices and 6n edges.
The Wagner graph is a cubic Hamiltonian graph and can be defined by the LCF notation [4] 8.It is an instance of an Andrásfai graph, a type of circulant graph in which the vertices can be arranged in a cycle and each vertex is connected to the other vertices whose positions differ by a number that is 1 (mod 3).