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Minimum degree growth of the iterated line graph. (English) Zbl 1072.05566
In the paper is proven a conjecture of L’. Niepel, M. Knor and L’. Soltés [Ars Comb. 43, 193-202 (1996; Zbl 0881.05059)] that for graphs different from paths the minimum degree \(\delta _k\) in the \(k\)th iterated line graph satisfy the recurrence \(\delta _k=2\delta _{k-1}-2\) if \(k\) is large enough.
The result and its proof directly reflects the previous work [J. Comb. 6, 381-389 (1999; Zbl 0920.05058)] on the maximum degree.

MSC:
05C75 Structural characterization of families of graphs
05C12 Distance in graphs
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