|
| |
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,3
|
|
|
COMMENTS
|
Sources for values a(n), from A. L. Liestman:
n.....Source
1-16: Farley, Hedetniemi, Mitchell and Proskurowski
17: Hedetniemi and Mitchell "Census"
18-19: Xiao and Wang (reported in Bermond, Hell, Liestman and Peters)
20-23: Maheo and Sacle
24-25: Bermond, Hell, Liestman and Peters
26-29: Sacle (in Discrete Applied Math. 150, pp. 359-360, 1996); the value for n=26 was found independently by Chen (unpublished) and by Zhou and Zhang
30-31: Bermond, Hell, Liestman and Peters
32: Farley, Hedetniemi, Mitchell and Proskurowski
33-34: Weng and Ventura (in Telecomm. Systems 3, pp. 259-293, 1995)
35-36: Bermond, Fraigniaud and Peters
37-40: Bermond, Hell, Liestman and Peters
41-46: Bermond, Fraigniaud and Peters
47-48: Bermond, Fraigniaud and Peters
See Bermond, Fraigniaud and Peters for details of other references
|
|
|
REFERENCES
|
Bermond, Jean-Claude; Fraigniaud, Pierre; and Peters, Joseph G., Antepenultimate broadcasting Networks 26 (1995), 125-137.
Bermond, Jean-Claude; Hell, Pavol; Liestman, Arthur L.; Peters, Joseph G. Broadcasting in bounded degree graphs. SIAM J. Discrete Math. 5 (1992), no. 1, 10-24.
Farley, Arthur; Hedetniemi, Stephen; Mitchell, Sandra; Proskurowski, Andrzej Minimum broadcast graphs. Discrete Math. 25 (1979), 189-193.
S. M. Hedetniemi, S. T. Hedetniemi and A. L. Liestman, A survey of gossiping and broadcasting in communication networks, Networks, 18 (1988), 319-349.
A. L. Liestman and J. G. Peters, Broadcast networks of bounded degree, SIAM J. Discrete Math., 1 (1988), 531-540.
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), 275-285.
Mitchell, Sandra and Hedetniemi, Stephen, A census of minimum broadcast graphs. J. Combin. Inform. System Sci. 5 (1980), no. 2, 141-151.
Sacle, J.-F., Lower bounds for the size in four families of minimum broadcast graphs. Selected papers in honour of Paul Erdős on the occasion of his 80th birthday (Keszthely, 1993). Discrete Math. 150 (1996), 359-369.
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), 1023-1026.
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(2^k) = k*2^(k-1), a(2^k-2) = (k-1)*(2^(k-1)-1).
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,more,nice
|
|
|
AUTHOR
|
|
|
|
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
|
| |
|
|
