International Journal of Engineering Research in Electronics and Communication Engineering

On Strong (G,D) Number of Middle Graphs

Author : A.Sony ¹ M.Mahalakshmi ² K.Palani ³ S.Kalavathi ⁴

Date of Publication :20th April 2018

Abstract: (G,D)-number of graphs was introduced by Palani K and Nagarajan A . Let G be a (V,E) graph. A subset D of V(G) is said to be a (G,D)-set of G if it is both a dominating and a geodetic set of G. A dominating set is said to be a strong dominating set of G if it strongly dominates all the vertices of its complement. In this paper, we introduce the concept strong (G,D) number of middle graph and find the same for some standard graphs and its bounds

Reference :

1. uckley F, Harary F and Quintas V L, Extremal results on the geodetic number of a graph, Scientia, volume A2 (1988), 17-26.
2. Chartrand G, Harary F and Zhang P, Geodetic sets in graphs, Discussiones Mathematicae Graph theory, 20 (2000), 129-138e
3. Chartrand G, Harary F and Zhang P, On the Geodetic number of a graph, Networks, Volume 39(1) (2002), 1-6.
4. Chartrand G, Zhang P and Harary F, Extremal problems in Geodetic graph Theory, Congressus Numerantium 131 (1998), 55-66.
5. T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Fundamentals Of Domination in graphs, Marcel Decker, Inc., New York 1998
6. Ore.O Theory of Graphs, American Mathematical Society Colloquium Publication 38 (American Mathematical Society Providence RI) 1962.
7. Palani .K and Kalavathi. S, (G,D) – Number of some special graphs, International Journal Of Engineering and Mathematical Sciences January-June 2014, Volume 5,Issue1, pp.7-15ISSN(Print) – 2319 – 4537, (Online) – 2319 – 4545.
8. Palani. K and Nagarajan. A (G,D) – number of graphs,International Journal Of Engineering and Mathematics Research. ISSN 0976 – 5840 Volume 3(2011), pp 285 -299.
9. Palani. K ,Nagarajan. A and Mahadevan. G, Results connecting domination, geodetic and (G,D)– number of graph, International Journal Of Combinatorial graph theory and applications, Volume 3, No.1, January – June (2010)(pp.51 -59).
10. Santhaana Gomathi C, Palani K and Kalavathi S, Strong (G,D)-Number of a graph– communicated.
11. Selvalakshmi V, Susi Vinnarasi G, Palani K and Kalavathi S, Strong (G,D)-Number of Inflated graphs - communicated.
12. Velammal S, Rajalakshmi S, Palani K and Kalavathi S, Strong (G,D)-Number of Product graphs-communicated.