Signed (b,k)-Edge Covers in Graphs

A. N. Ghameshlou, A. Khodkar, R. Saei, S.M. Sheikholeslami

.

DOI: 10.4236/iim.2010.22017                

Abstract

Let be a simple graph with vertex set and edge set . Let have at least vertices of degree at least , where and are positive integers. A function is said to be a signed -edge cover of if for at least vertices of , where . The value , taking over all signed -edge covers of is called the signed -edge cover number of and denoted by . In this paper we give some bounds on the signed -edge cover number of graphs.

Keywords

Signed Star Dominating Function, Signed Star Domination Number, Signed -edge Cover, Signed -edge Cover Number

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	D. K?nig, “über trennende knotenpunkte in graphen (nebst anwendungen auf determinanten und matrizen),” Acta Litterarum ac Scientiarum Regiae Universitatis Hungaricae Francisco-Josephinae, Sectio Scientiarum Mathematicarum [Szeged], Vol. 6, pp. 155–179, 1932– 1934.
[2]	R. Rado, “Studien zur kombinatorik,” Mathematische Zeitschrift, German, Vol. 36, pp. 424–470, 1933.
[3]	T. Gallai, “über extreme Punkt-und Kantenmengen (German),” Ann. Univ. Sci. Budapest. E?tv?s Sect. Math., Vol. 2, pp. 133–138, 1959.
[4]	R. Z. Norman and M. O. Rabin, “An algorithm for a minimum cover of a graph,” Proceedings of the American Mathematical Society, Vol. 10, pp. 315–319, 1959.
[5]	A. Schrijver, “Combinatorial optimization: Polyhedra and Efficiency,” Springer, Berlin, 2004.
[6]	D. B. West, “Introduction to graph theory,” Prentice- Hall, Inc., 2000.
[7]	B. Xu, “On signed edge domination numbers of graphs,” Discrete Mathematics, Vol. 239, pp. 179–189, 2001.
[8]	C. Wang, “The signed star domination numbers of the Cartesian product,” Discrete Applied Mathematics, Vol. 155, pp. 1497–1505, 2007.
[9]	B. Xu, “Note on edge domination numbers of graphs,” Discrete Mathematics, Vol. 294, pp. 311–316, 2005.
[10]	B. Xu, “Two classes of edge domination in graphs,” Discr- ete Applied Mathematics, Vol. 154, pp. 1541–1546, 2006.
[11]	R. Saei and S. M. Sheikholeslami, “Signed star -subdomination numbers in graph,” Discrete Applied Mathematics, Vol. 156, pp. 3066–3070, 2008.
[12]	A. Bonato, K. Cameron, and C. Wang, “Signed b-edge covers of graphs (manuscript)”.