Bicubic Graph
A bicubic graph is a bipartite cubic graph.
Tutte (1971) conjectured that all 3-connected bicubic graphs are Hamiltonian (the Tutte conjecture), but a number of bicubic nonhamiltonian graphs have subsequently been discovered.
BicubicGraphs
The numbers of simple bicubic graphs on n=2, 4, ... nodes are 0, 0, 1, 1, 2, 5, 13, 38, 149, ... (OEIS A006823), the first few of which are illustrated above.
The following table summarizes some named bicubic graphs.
graph G |V(G)|
Pappus
graph 18
Tutte 8-cage 30
Dyck graph 32
Gray
graph 54
Foster
graph 90
Tutte 12-cage 126
See also
Bipartite Graph, Cubic Graph, Tutte ConjectureExplore with Wolfram|Alpha
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References
Sloane, N. J. A. Sequences A006823/M1450 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
Bicubic GraphCite this as:
Weisstein, Eric W. "Bicubic Graph." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BicubicGraph.html