Reverse Total Signed Vertex Domination in Graphs

Author(s)
Wensheng Li

Affiliation(s)

Department of Mathematics and Information Sciences, Langfang Teachers College, Langfang, China.

Department of Mathematics and Information Sciences, Langfang Teachers College, Langfang, China.

ABSTRACT

Let be a simple graph with vertex set*V* and edge set *E.* A function is said to be a reverse total signed vertex dominating function if for every , the sum of function values over v and the elements incident to v is less than zero. In this paper, we present some upper bounds of reverse total signed vertex domination number of a graph and the exact values of reverse total signed vertex domination number of circles, paths and stars are given.

Let be a simple graph with vertex set

Cite this paper

W. Li, "Reverse Total Signed Vertex Domination in Graphs,"*Open Journal of Discrete Mathematics*, Vol. 3 No. 1, 2013, pp. 53-55. doi: 10.4236/ojdm.2013.31011.

W. Li, "Reverse Total Signed Vertex Domination in Graphs,"

References

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[2] T. T. Chelvam and G. Kalaimurugan, “Bounds for Domination Parameters in Cayley Graphs on Dihedral Group,” Open Journal of Discrete Mathematics, Vol. 2, No. 1, 2012, pp. 5-10. doi:10.4236/ojdm.2012.21002

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[7] Z. Zhang, B. Xu, Y. Li and L. Liu, “A Note on the Lower Bounds of Signed Domination Number of a Graph,” Discrete Mathematics, Vol. 195, No. 1, 1999, pp. 295-298. doi:10.1016/S0012-365X(98)00189-7

[8] X. Z. Lv, “Total Signed Domination Numbers of Graphs,” Science in China A: Mathematics, Vol. 37, 2007, pp. 573-578.

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[1] J. A. Bondy and V. S. R. Murty, “Graph Theory with Application,” Elsevier, Amsterdam, 1976.

[2] T. T. Chelvam and G. Kalaimurugan, “Bounds for Domination Parameters in Cayley Graphs on Dihedral Group,” Open Journal of Discrete Mathematics, Vol. 2, No. 1, 2012, pp. 5-10. doi:10.4236/ojdm.2012.21002

[3] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, “Fundamentals of Domination in Graphs,” Marcel Dekker, New York, 1998.

[4] G. T. Wang and G. Z. Liu, “Rainbow Matchings in Properly Colored Bipartite Graphs,” Open Journal of Discrete Mathematics, Vol. 2, No. 2, 2012, pp. 62-64. doi:10.4236/ojdm.2012.22011

[5] J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater, “Signed Domination in Graphs,” Combinatorics, Graph Theory, Applications, Vol. 1, 1995, pp. 311-322.

[6] O. Favaron, “Signed Domination in Regular Graphs,” Discrete Mathematics, Vol. 158, No. 1, 1996, pp. 287-293. doi:10.1016/0012-365X(96)00026-X

[7] Z. Zhang, B. Xu, Y. Li and L. Liu, “A Note on the Lower Bounds of Signed Domination Number of a Graph,” Discrete Mathematics, Vol. 195, No. 1, 1999, pp. 295-298. doi:10.1016/S0012-365X(98)00189-7

[8] X. Z. Lv, “Total Signed Domination Numbers of Graphs,” Science in China A: Mathematics, Vol. 37, 2007, pp. 573-578.

[9] X. Z. Lv, “A Lower Bound on the Total Signed Domination Numbers of Graphs,” Science in China Series A: Mathematics, Vol. 50, 2007, pp. 1157-1162.