A 1-relaxed minimum broadcast graph on 15 vertices

In 1998, Shastri studied the sparsest possible broadcast graphs in which broadcasting can be accomplished in slightly more than the optimal time of ⌜ log 2 n⌝ . In particular, they constructed the sparsest possible time-relaxed broadcast graphs for small n (≤ 14) and very sparse time-relaxed broadca...

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Bibliographic Details
Published inApplied mathematics letters Vol. 17; no. 3; pp. 249 - 252
Main Authors Yao, Tianxing, Zhou, Guofei, Zhou, Jianguo
Format Journal Article
LanguageEnglish
Published Oxford Elsevier Ltd 01.03.2004
Elsevier
Subjects
Broadcasting
Combinatorics
Combinatorics. Ordered structures
Communication
Exact sciences and technology
Graph theory
Mathematics
Networks
Sciences and techniques of general use
Time-relaxed broadcast
Broadcasting
Networks
Time-relaxed broadcast
Communication
Edge(graph)
Graph theory
Minimal graph
Applied mathematics
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Summary:In 1998, Shastri studied the sparsest possible broadcast graphs in which broadcasting can be accomplished in slightly more than the optimal time of ⌜ log 2 n⌝ . In particular, they constructed the sparsest possible time-relaxed broadcast graphs for small n (≤ 14) and very sparse time-relaxed broadcast graphs for larger n (≤ 65). Let B t ( n) be the number of edges in the sparsest possible graph on n vertices in which broadcasting can be accomplished in t additional steps than the optimal (i.e., in ⌜ log 2 n⌝ + t steps), they conjectured that B 1(15) = 18. In this paper, we give a 1-relaxed minimum broadcast graph on 15 vertices which shows that B 1(15) = 17, thus reject the conjecture.
ISSN:0893-9659
1873-5452
DOI:10.1016/S0893-9659(04)90059-6