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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 ...
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.
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 ...
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 ...
In the mathematical field of graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. [1] It is named after Girard Desargues, arises from several different combinatorial constructions, has a high level of symmetry, is the only known non-planar cubic partial cube, and has been applied in chemical databases.
In the mathematical field of graph theory, the Frucht graph is a cubic graph with 12 vertices, 18 edges, and no nontrivial symmetries. [1] It was first described by Robert Frucht in 1939. [2] The Frucht graph is a pancyclic, Halin graph with chromatic number 3, chromatic index 3, radius 3, and diameter 4.
In a cubic graph with a perfect matching, the edges that are not in the perfect matching form a 2-factor. By orienting the 2-factor, the edges of the perfect matching can be extended to paths of length three, say by taking the outward-oriented edges. This shows that every cubic, bridgeless graph decomposes into edge-disjoint paths of length ...
In the mathematical field of graph theory, the F26A graph is a symmetric bipartite cubic graph with 26 vertices and 39 edges. [1] It has chromatic number 2, chromatic index 3, diameter 5, radius 5 and girth 6. [2] It is also a 3-vertex-connected and 3-edge-connected graph. The F26A graph is Hamiltonian and can be described by the LCF notation ...
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