Connectivity Properties of Generalized K4-Hypercubes
Keyword(s):
We consider the class of generalized hypercubes constructed recursively from the graph [Formula: see text] by repeatedly taking two copies of such a graph with a perfect matching added in between. We show that all graphs obtained this way have very good connectivity properties. They are all maximally connected, and even when linearly many vertices are deleted, the remaining graph will have a large connected component with only a few vertices in other components. We also show examples that we can delete more vertices in certain graphs in this class to get the second largest component to have certain sizes, including the case when we get two components of equal size. We conjecture that these examples are best possible.
2015 ◽
Vol 15
(01n02)
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pp. 1550007
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Keyword(s):
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2015 ◽
Vol 10
(10)
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pp. 995
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2010 ◽
Vol 30
(6)
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pp. 1616-1618
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2009 ◽
Vol 28
(12)
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pp. 3150-3153
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