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On the Crossing Number of Generalized Fat Trees

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Informatics Engineering and Information Science (ICIEIS 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 253))

Abstract

The crossing number of a graph G is the minimum number of crossings of its edges among the drawings of G in the plane and is denoted by cr(G). Bhatt and Leighton proved that the crossing number of a network is closely related to the minimum layout area required for the implementation of the VLSI circuit for that network. In this paper, we find an upper bound for the crossing number of a special case of the generalized fat tree based on the underlying graph model found in the literature. We also improve this bound for a new drawing of the same structure. The proofs are based on the drawing rules introduced in this paper.

This work is supported by The Minor Project - No.F.1-2/2010-2011 (RO/SERO/MRP) PNO. 345 of University Grants Commission, Hyderabad, India.

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Authors and Affiliations

  1. Department of Mathematics, Loyola College, Chennai, India

    Bharati Rajan & Indra Rajasingh

  2. Department of Mathematics, Queen Mary’s College, Chennai, India

    P. Vasanthi Beulah

Authors
  1. Bharati Rajan
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  2. Indra Rajasingh
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  3. P. Vasanthi Beulah
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Editor information

Editors and Affiliations

  1. Advanced Informatics School (UTM AIS), UTM International Campus, 54100, Kuala Lumpur, Malaysia

    Azizah Abd Manaf , Shamsul Sahibuddin , Rabiah Ahmad  & Salwani Mohd Daud , ,  & 

  2. Information Systems Department, King Saud University, Riyadh, Saudi Arabia

    Eyas El-Qawasmeh

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© 2011 Springer-Verlag Berlin Heidelberg

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Rajan, B., Rajasingh, I., Vasanthi Beulah, P. (2011). On the Crossing Number of Generalized Fat Trees. In: Abd Manaf, A., Sahibuddin, S., Ahmad, R., Mohd Daud, S., El-Qawasmeh, E. (eds) Informatics Engineering and Information Science. ICIEIS 2011. Communications in Computer and Information Science, vol 253. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25462-8_40

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  • DOI: https://doi.org/10.1007/978-3-642-25462-8_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25461-1

  • Online ISBN: 978-3-642-25462-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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