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Conference on Algorithms and Discrete Applied Mathematics

CALDAM 2017: Algorithms and Discrete Applied Mathematics pp 193–204Cite as

Broadcast Graphs Using New Dimensional Broadcast Schemes for Knödel Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10156))

Abstract

Broadcasting is an information disseminating process of distributing a message from an originator vertex v of graph \(G=(V,E)\) to all of its vertices. The broadcast time of vertex v is the minimum possible time required to broadcast from v in graph G. A graph G on n vertices is called broadcast graph if broadcasting from any originator in G can be accomplished in \(\lceil \log n\rceil \) time. A broadcast graph with the minimum number of edges is called minimum broadcast graph. The number of edges in a minimum broadcast graph on n vertices is denoted by B(n). Finding the values of B(n) is very difficult. A large number of papers present techniques to construct broadcast graphs and to obtain upper bounds on B(n). In this paper, we first find new dimensional broadcast schemes for Knödel graphs, and then use them to give a general upper bound on B(n) for almost all odd n.

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Authors and Affiliations

  1. Concordia University, Montreal, Québec, H3G 1M8, Canada

    Hovhannes A. Harutyunyan & Zhiyuan Li

Authors
  1. Hovhannes A. Harutyunyan
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  2. Zhiyuan Li
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Correspondence to Zhiyuan Li .

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Editors and Affiliations

  1. University of Lethbridge, Lethbridge, Alberta, Canada

    Daya Gaur

  2. Indian Institute of Technology Madras, Chennai, India

    N.S. Narayanaswamy

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Harutyunyan, H.A., Li, Z. (2017). Broadcast Graphs Using New Dimensional Broadcast Schemes for Knödel Graphs. In: Gaur, D., Narayanaswamy, N. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2017. Lecture Notes in Computer Science(), vol 10156. Springer, Cham. https://doi.org/10.1007/978-3-319-53007-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-53007-9_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-53006-2

  • Online ISBN: 978-3-319-53007-9

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