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The Petersen graph is a cubic graph. The complete bipartite graph, is an example of a bicubic graph. In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs.
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.
Cubic symmetric graphs (The Foster Census). Data files for all cubic symmetric graphs up to 768 vertices, and some cubic graphs with up to 1000 vertices. Gordon Royle, updated February 2001, retrieved 2009-04-18. Trivalent (cubic) symmetric graphs on up to 10000 vertices. Marston Conder, 2011.
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.
In the mathematical field of graph theory, Tietze's graph is an undirected cubic graph with 12 vertices and 18 edges. It is named after Heinrich Franz Friedrich Tietze, who showed in 1910 that the Möbius strip can be subdivided into six regions that all touch each other – three along the boundary of the strip and three along its center line – and therefore that graphs that are embedded ...
A cubic graph (all vertices have degree three) of girth g that is as small as possible is known as a g-cage (or as a (3,g)-cage).The Petersen graph is the unique 5-cage (it is the smallest cubic graph of girth 5), the Heawood graph is the unique 6-cage, the McGee graph is the unique 7-cage and the Tutte eight cage is the unique 8-cage. [3]
2. The Frucht graph, one of the two smallest cubic graphs with no nontrivial symmetries. 3. Frucht's theorem that every finite group is the group of symmetries of a finite graph. full Synonym for induced. functional graph A functional graph is a directed graph where every vertex has out-degree one. Equivalently, a functional graph is a maximal ...
In the mathematical field of graph theory, the flower snarks form an infinite family of snarks introduced by Rufus Isaacs in 1975. [1] As snarks, the flower snarks are connected, bridgeless cubic graphs with chromatic index equal to 4. The flower snarks are non-planar and non-Hamiltonian.