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Connectivity of iterated line graphs. (English) Zbl 1009.05086
Summary: We present lower bounds for the connectivity of the $$i$$-iterated line graph $$L^i(G)$$ of a graph $$G$$. We prove that if $$G$$ is a connected regular graph and $$i\geqslant 5$$, then the connectivity of $$L^i(G)$$ is equal to the degree of $$L^i(G)$$, that is, the connectivity of $$L^i(G)$$ attains its theoretical maximum (we remark that the bound on $$i$$ is best possible). Moreover, if a hypothesis on the growth of the minimum degree of the $$i$$-iterated line graph is true, then an analogous result is true for an arbitrary graph $$G$$ if $$i$$ is sufficiently large.

##### MSC:
 05C40 Connectivity
Full Text:
##### References:
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