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Flower Graph


FlowerGraphs

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 to 9. Flower graphs are unit-distance.

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

Different graphs are sometimes termed flower graphs by various authors.

Herbster and Pontil (2006) define a flower graph as a graph obtained by connecting the first vertex of a chain with p-1 vertices to the root vertex of an m-ary tree of depth one. The vertices of this graph can be indexed so that vertices 1 to p correspond to "stem vertices" and vertices p+1 to p+m to "petals."

Seoud and Youssef (2017) define a flower graph as the graph obtained from a helm graph by joining each pendent vertex to the central vertex (Gallian 2018).


See also

Flower Snark

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References

Gallian, J. "Dynamic Survey of Graph Labeling." Elec. J. Combin. DS6. Dec. 21, 2018. https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6.Herbster, M. and Pontil, M. "Prediction on a Graph with a Perception." In Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference (Ed. B. Schölkopf, J. Platt, and T. Hoffman). Cambridge, MA: MIT Press, pp. 577-584, 2006.Seoud, M. Z. and Youssef, M. A. "Harmonious Labelling of Helms and Related Graphs." Unpublished work. Jan. 2017. http://dx.doi.org/10.13140/RG.2.2.11041.61282.

Cite this as:

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

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