A Note on Edge-Domsaturation Number of a Graph
Affiliation(s)
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India.
Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli- 627 012, India.
ABSTRACT
The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.
The edge-domsaturation number ds'(G) of a graph G = (V, E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. In this paper, we characterize unicyclic graphs G with ds'(G) = q – Δ'(G) + 1 and investigate well-edge dominated graphs. We further define γ'–-critical, γ'+-critical, ds'–-critical, ds'+-critical edges and study some of their properties.
Cite this paper
D. Nidha and M. Kala, "A Note on Edge-Domsaturation Number of a Graph," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 109-113. doi: 10.4236/ojdm.2012.23021.
D. Nidha and M. Kala, "A Note on Edge-Domsaturation Number of a Graph," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 109-113. doi: 10.4236/ojdm.2012.23021.
References
[1] F. Harary, “Graph Theory,” Addison-Wesley Publishing Company, Boston, 1969. [2] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, “Fundamentals of Domination in Graphs,” Marcel Dekker, New York, 1998. [3] B. D. Acharya, “The Strong Domination Number of a Graph and Related Concepts,” Journal of Mathematical Physics, Vol. 14, No. 5, 1980, pp. 471-475. [4] S. Arumugam and R. Kala, “Domsaturation Number of a Graph,” Indian Journal of Pure and Applied Mathematics, Vol. 33, No. 11, 2002, pp. 1671-1676. [5] S. Arumugam and S. Velammal, “Edge Domination in Graphs,” Taiwanese Journal of Mathematics, Vol. 2, No. 2, 1998, pp. 173-179. [6] A. Finbow, B. L. Hartnell and R. Nowakowski, “Well Dominated Graphs: A Collection of Covered Ones,” Ars Combinatoria, Vol. 25, No. A, 1988, pp. 5-10.
[1] F. Harary, “Graph Theory,” Addison-Wesley Publishing Company, Boston, 1969. [2] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, “Fundamentals of Domination in Graphs,” Marcel Dekker, New York, 1998. [3] B. D. Acharya, “The Strong Domination Number of a Graph and Related Concepts,” Journal of Mathematical Physics, Vol. 14, No. 5, 1980, pp. 471-475. [4] S. Arumugam and R. Kala, “Domsaturation Number of a Graph,” Indian Journal of Pure and Applied Mathematics, Vol. 33, No. 11, 2002, pp. 1671-1676. [5] S. Arumugam and S. Velammal, “Edge Domination in Graphs,” Taiwanese Journal of Mathematics, Vol. 2, No. 2, 1998, pp. 173-179. [6] A. Finbow, B. L. Hartnell and R. Nowakowski, “Well Dominated Graphs: A Collection of Covered Ones,” Ars Combinatoria, Vol. 25, No. A, 1988, pp. 5-10.