Combinatorica`
Combinatorica`
CageGraph
As of Version 10, most of the functionality of the Combinatorica package is built into the Wolfram System. »
CageGraph[k,r]
gives a smallest k-regular graph of girth r for certain small values of k and r. For k=3, r can be 3, 4, 5, 6, 7, 8, or 10. For k=4 or 5, r can be 3, 4, 5, or 6.
CageGraph[r]
gives CageGraph[3,r].
Details and Options
- CageGraph functionality is now available in the built-in Wolfram Language function GraphData.
- To use CageGraph, you first need to load the Combinatorica Package using Needs["Combinatorica`"].
Examples
Basic Examples (1)Summary of the most common use cases
In[1]:=1

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https://wolfram.com/xid/0s1h88pswq-guoqy5
Out[1]=1

Wolfram Research (2012), CageGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
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Wolfram Research (2012), CageGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
Text
Wolfram Research (2012), CageGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
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Wolfram Research (2012), CageGraph, Wolfram Language function, https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
CMS
Wolfram Language. 2012. "CageGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
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Wolfram Language. 2012. "CageGraph." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html.
APA
Wolfram Language. (2012). CageGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html
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Wolfram Language. (2012). CageGraph. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html
BibTeX
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@misc{reference.wolfram_2025_cagegraph, author="Wolfram Research", title="{CageGraph}", year="2012", howpublished="\url{https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html}", note=[Accessed: 10-July-2025
]}
BibLaTeX
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@online{reference.wolfram_2025_cagegraph, organization={Wolfram Research}, title={CageGraph}, year={2012}, url={https://reference.wolfram.com/language/Combinatorica/ref/CageGraph.html}, note=[Accessed: 10-July-2025
]}