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Call For Paper : Vol 11, Issue 03, March 2024

ISSN : 2456-1304 (Online)

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Vol 11, Issue 03, March 2024

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Strong (G, D) - Number of a Graph

Author : C. Santhaana Gomathi 1 K. Palani 2 S. Kalavathi 3

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Date of Publication :20th April 2018

Abstract: (G D) – number of a graph 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 G. In this paper, we introduce the concept Strong (G,D)- number of a graph and find the same for some standard graphs and its bounds

Reference :

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    11.  

    1. Buckley 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, DiscussionesMathematicae 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, CongressusNumerantium 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,Issue-

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