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theta_0 Graph


Theta0

The biconnected graph theta_0 on seven nodes and seven edges illustrated above. It has chromatic polynomial

 pi_(theta_0)(z)=z^7-8z^6+28z^5-56z^4+68z^3-47z^2+14z

and chromatic number gamma(theta_0)=3.

The puz-graph of a finite simple biconnected graph G that is not polygonal always has two connected components if G is bipartite; otherwise (with the exception of theta_0), puz(G) is connected. Surprisingly, the puz-graph of the theta_0 graph is the sole exception, having six connected components instead of a single component.


See also

15 Puzzle, Puz-Graph

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References

Archer, A. F. "A Modern Treatment of the 15 Puzzle." Amer. Math. Monthly 106, 793-799, 1999.Wilson, R. M. "Graph Puzzles, Homotopy, and the Alternating Group." J. Combin. Th. Ser. B 16, 86-96, 1974.

Cite this as:

Weisstein, Eric W. "theta_0 Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Theta-0Graph.html

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