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On broadcasting in unicyclic graphs

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Abstract

Broadcasting is an information dissemination problem in a connected network, in which one node, called the originator, disseminates a message to all other nodes by placing a series of calls along the communication lines of the network. Finding the broadcast time of a vertex in an arbitrary graph is NP-complete. The polynomial time solvability is shown only for trees. In this paper we present a linear algorithm that determines the broadcast time of any originator in an arbitrary unicyclic graph. As a byproduct, we find a broadcast center of the unicyclic graph. We also present an O(|V|+k 2) algorithm to find the broadcast time of an arbitrary unicyclic graph, where k is the length of the cycle. In the last section we give tight lower and upper bounds on broadcast time of a spanning tree based on the broadcast time of the unicyclic graph.

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Authors and Affiliations

  1. Department of Computer Science, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada

    Hovhannes A. Harutyunyan & Edward Maraachlian

Authors
  1. Hovhannes A. Harutyunyan
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  2. Edward Maraachlian
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Correspondence to Hovhannes A. Harutyunyan.

Additional information

The results of Sects. 2, 3 and most of the proofs in Sects. 2, 3 of this paper are presented by Harutyunyan and Maraachlian (Proceedings of 13th annual COCOON, pp. 372–383, 2007). All results in Sects. 4, 5 and the complete proof of Theorem 3 are new results.

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Harutyunyan, H.A., Maraachlian, E. On broadcasting in unicyclic graphs. J Comb Optim 16, 307–322 (2008). https://doi.org/10.1007/s10878-008-9160-2

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