

A007192


Number of edges in minimal broadcast graph with n nodes.
(Formerly M0508)


1



0, 1, 2, 4, 5, 6, 8, 12, 10, 12, 13, 15, 18, 21, 24, 32, 22, 23, 25, 26, 28, 31
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OFFSET

1,3


COMMENTS

Sources for values a(n), from A. L. Liestman:
n.....Source
116: Farley, Hedetniemi, Mitchell and Proskurowski
17: Hedetniemi and Mitchell "Census"
1819: Xiao and Wang (reported in Bermond, Hell, Liestman and Peters)
2023: Maheo and Sacle
2425: Bermond, Hell, Liestman and Peters
2629: Sacle (in Discrete Applied Math. 150, pp. 359360, 1996); the value for n=26 was found independently by Chen (unpublished) and by Zhou and Zhang
3031: Bermond, Hell, Liestman and Peters
32: Farley, Hedetniemi, Mitchell and Proskurowski
3334: Weng and Ventura (in Telecomm. Systems 3, pp. 259293, 1995)
3536: Bermond, Fraigniaud and Peters
3740: Bermond, Hell, Liestman and Peters
4146: Bermond, Fraigniaud and Peters
4748: Bermond, Fraigniaud and Peters
See Bermond, Fraigniaud and Peters for details of other references


REFERENCES

Bermond, JeanClaude; Fraigniaud, Pierre; and Peters, Joseph G., Antepenultimate broadcasting Networks 26 (1995), 125137.
Bermond, JeanClaude; Hell, Pavol; Liestman, Arthur L.; Peters, Joseph G. Broadcasting in bounded degree graphs. SIAM J. Discrete Math. 5 (1992), no. 1, 1024.
Farley, Arthur; Hedetniemi, Stephen; Mitchell, Sandra; Proskurowski, Andrzej Minimum broadcast graphs. Discrete Math. 25 (1979), 189193.
S. M. Hedetniemi, S. T. Hedetniemi and A. L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks, 18 (1988), 319349.
A. L. Liestman and J. G. Peters, Broadcast networks of bounded degree, SIAM J. Discrete Math., 1 (1988), 531540.
Maheo, M. and Sacle, J.F., Some minimum broadcast graphs, in Proceedings International Workshop on Broadcasting and Gossiping 1990 (Sechelt, BC). Discrete Appl. Math. 53 (1994), 275285.
Mitchell, Sandra and Hedetniemi, Stephen, A census of minimum broadcast graphs. J. Combin. Inform. System Sci. 5 (1980), no. 2, 141151.
Sacle, J.F., Lower bounds for the size in four families of minimum broadcast graphs. Selected papers in honour of Paul ErdÅ‘s on the occasion of his 80th birthday (Keszthely, 1993). Discrete Math. 150 (1996), 359369.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J.G. Zhou and K.M. Zhang, A minimum broadcast graph on 26 vertices, Appl. Math. Lett. 14 (2001), 10231026.


LINKS

Table of n, a(n) for n=1..22.


FORMULA

a(2^k) = k*2^(k1), a(2^k2) = (k1)*(2^(k1)1).


CROSSREFS

Sequence in context: A099247 A192583 A240064 * A081354 A119792 A085834
Adjacent sequences: A007189 A007190 A007191 * A007193 A007194 A007195


KEYWORD

nonn,more,nice


AUTHOR

Simon Plouffe


EXTENSIONS

Entry revised (and corrected and extended) by N. J. A. Sloane Mar 20 2005, using information kindly supplied by Art Liestman.
Upper bounds for the next three entries a(23), a(24), a(25) are 34, 36, 40.


STATUS

approved



