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Structural Properties of Subdivided-Line Graphs

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Combinatorial Algorithms (IWOCA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8288))

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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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Authors and Affiliations

  1. Institute of Socio-Arts and Sciences, The University of Tokushima, 1–1 Minamijosanjima, Tokushima, 770–8502, Japan

    Toru Hasunuma

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  1. Toru Hasunuma
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Editors and Affiliations

  1. UFR des Sciences et Techniques, LITIS, Université de Rouen, 76821, EA 4180, Mont Saint Aignan Cedex, France

    Thierry Lecroq  & Laurent Mouchard  & 

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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