Abstract
Motivated by self-similar structures of Sierpiński graphs, we newly introduce the subdivided-line graph operation Γ and define the n-iterated subdivided-line graph Γn(G) of a graph G. We then study structural properties of subdivided-line graphs such as edge-disjoint Hamilton cycles, hub sets, connected dominating sets, and completely independent spanning trees which can be applied to problems on interconnection networks. From our results, the maximum number of edge-disjoint Hamilton cycles, the minimum cardinality of a hub set, the minimum cardinality of a connected dominating set, and the maximum number of completely independent spanning trees in Sierpiński graphs are obtained as corollaries. In particular, our results for edge-disjoint Hamilton cycles and hub sets on iterated subdivided-line graphs are generalizations of the previously known results on Sierpiński graphs, while our proofs are simpler than those for Sierpiński graphs.
This work was supported by JSPS KAKENHI 25330015.
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Hasunuma, T. (2013). Structural Properties of Subdivided-Line Graphs. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_19
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DOI: https://doi.org/10.1007/978-3-642-45278-9_19
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