Signed (b,k)-Edge Covers in Graphs

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.

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

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

Cite this paper

nullA. Ghameshlou, A. Khodkar, R. Saei and S. Sheikholeslami, "Signed (b,k)-Edge Covers in Graphs,"*Intelligent Information Management*, Vol. 2 No. 2, 2010, pp. 143-148. doi: 10.4236/iim.2010.22017.

nullA. Ghameshlou, A. Khodkar, R. Saei and S. Sheikholeslami, "Signed (b,k)-Edge Covers in Graphs,"

References

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[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)”.

[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)”.