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On Strong Menger-Connectivity of Star Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2204))

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Abstract

Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a d-regular graph. We say that G is strongly Menger-connected if for any copy G f of G with at most d - 2 nodes removed, every pair of nodes u and v in G f are connected by mindeg f(u), deg f(v) node-disjoint paths in G f, where deg f(u) and deg f(v) are the degrees of the nodes u and v in G f, respectively.We show that the star graphs, which are a recently proposed attractive alternative to the widely used hypercubes as network models, are strongly Menger-connected. An algorithm of optimal running time is developed that constructs the maximum number of node-disjoint paths of nearly optimal length in star graphs with faults.

This work is supported in part by NSF under Grant CCR-0000206.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843-3112, USA

    ]Eunseuk Oh & Jianer Chen

Authors
  1. ]Eunseuk Oh
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  2. Jianer Chen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rostock, 18051, Rostock, Germany

    Andreas Brandstädt  & Van Bang Le  & 

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© 2001 Springer-Verlag Berlin Heidelberg

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Oh, ]., Chen, J. (2001). On Strong Menger-Connectivity of Star Graphs. In: Brandstädt, A., Le, V.B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2001. Lecture Notes in Computer Science, vol 2204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45477-2_25

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  • DOI: https://doi.org/10.1007/3-540-45477-2_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42707-0

  • Online ISBN: 978-3-540-45477-9

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