In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the start of the Foster census. Many well-known individual graphs are cubic and symmetric, including the utility graph, … See more

Cubic graphs arise naturally in topology in several ways. For example, the cubic graphs with 2g-2 vertices describe the different ways of … See more

The pathwidth of any n-vertex cubic graph is at most n/6. The best known lower bound on the pathwidth of cubic graphs is 0.082n. It is not known how to reduce this gap between this See more

• Table of simple cubic graphs See more

According to Brooks' theorem every connected cubic graph other than the complete graph K4 has a vertex coloring with at most three colors. Therefore, every connected cubic graph other than K4 has an independent set of at least n/3 vertices, where n is the … See more

There has been much research on Hamiltonicity of cubic graphs. In 1880, P.G. Tait conjectured that every cubic polyhedral graph has a Hamiltonian circuit. See more

Several researchers have studied the complexity of exponential time algorithms restricted to cubic graphs. For instance, by applying dynamic programming to a path decomposition of … See more