On broadcasting in unicyclic graphs

Hovhannes A. Harutyunyan () and Edward Maraachlian
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Hovhannes A. Harutyunyan: Concordia University
Edward Maraachlian: Concordia University

Journal of Combinatorial Optimization, 2008, vol. 16, issue 3, No 8, 307-322

Abstract: 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.

Keywords: Broadcasting; Algorithms; Unicyclic graph (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10878-008-9160-2

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