Flower Snark


The flower snarks, denoted J_n for n=5, 7, 9, ..., are a family of graphs discovered by Isaacs (1975) which are snarks. The construction for flower snarks may be generalized to all (i.e., not just odd) integer n>=5. In this work, such graphs are termed flower graphs.

J_5 appears in Scheinerman and Ullman (2011, p. 96) as an example of a graph with edge chromatic number and fractional edge chromatic number (4 and 3, respectively) both integers but not equal.

Flower snarks are unit-distance. They are also maximally nonhamiltonian for odd n>=3 (Clark and Entringer 1983).

Precomputed properties of flower snarks are implemented in the Wolfram Language as GraphData[{"Flower", n}].

See also

Flower Graph, Snark

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Clark, L. and Entringer, R. "Smallest Maximally Nonhamiltonian Graphs." Periodica Math. Hungarica 14, 57-68, 1983.Holton, D. A. and Sheehan, J. The Petersen Graph. Cambridge, England: Cambridge University Press, pp. 82 and 97-100, 1993.Isaacs, R. "Infinite Families of Nontrivial Trivalent Graphs Which Are Not Tait Colorable." Amer. Math. Monthly 82, 221-239, 1975.Scheinerman, E. R. and Ullman, D. H. Fractional Graph Theory A Rational Approach to the Theory of Graphs. New York: Dover, 2011.West, D. B. Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, p. 306, 2000.

Cite this as:

Weisstein, Eric W. "Flower Snark." From MathWorld--A Wolfram Web Resource.

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