This Article 
 Bibliographic References 
 Add to: 
On the Genus of Star Graphs
June 1994 (vol. 43 no. 6)
pp. 755-759

The star graph has recently been suggested as an alternative to the hypercube. The star graph has a rich structure and symmetry properties as well as desirable fault-tolerant characteristics. The star graph's maximum vertex degree and diameter, viewed as functions of network size, grow less rapidly than the corresponding measures in a hypercube. We investigate the genus of the star graph and compare it with the genus of the hypercube.

[1] S. B. Akers, D. Harel, and B. Krishnamurthy, "The star graph: An attractive alternative to then-cube," inProc. Int. Conf. Parallel Processing, 1987, pp. 393-400.
[2] S. B. Akers and B. Krishnamurthy, "A group theoretic model for symmetric interconnection networks,"IEEE Trans. Comput., vol. C-38, pp. 555-566, Apr. 1989.
[3] L. W. Beineke and F. Harary, "The genus of then-cube,"Canadian J. Math., vol. 17, pp. 494-496, 1965.
[4] G. Chartrand and L. Lesniak,Graphs and Digraphs. Wadsworth, Monterey, 1986.
[5] V. E. Mendia and D. Sarkar, "Optimal broadcasting on the star graph,"IEEE Trans. Parallel Distrib. Syst., vol. 3, pp. 389-396, Apr. 1992.
[6] G. Ringel, "Über drie kombinatorische Probleme amn-dimensionalen Würfel und Würfelgitter," inAbh. Math. Sem. Univ. Hambourg, vol. 10, pp. 10-19, 1955.

Index Terms:
hypercube networks; fault tolerant computing; reliability; genus of star graphs; hypercube; symmetry properties; fault-tolerant characteristics; maximum vertex degree.
D.A. Hoelzeman, S. Bettayeb, "On the Genus of Star Graphs," IEEE Transactions on Computers, vol. 43, no. 6, pp. 755-759, June 1994, doi:10.1109/12.286309
Usage of this product signifies your acceptance of the Terms of Use.