Minimal Roman dominating function

D. K Thakkar, Sanket Mukundbhai Badiyani


In this paper, the concept of Minimal Roman Dominating Function is considered. A characterization of a Minimal Roman Dominating Function has been given. It has also been proved that for any graph with vertices, the Upper Roman Domination Number is . It is also shown that if is a Minimal Roman Dominating Function then is a Roman Dominating Function for a graph without isolated vertices. We also prove that if and only if there is a Minimum Roman Dominating Function which does not assume value 1 at any vertex of .

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T.W. Haynes, S.T. Hedetniemi and P.J. Slater, Domination In graphs Advanced Topics, New York, 1998.

T.W .Haynes, S.T. Hedetniemi and P.J.Slater, Fundamental of Domination In graphs, Marcel Dekker, New York, 1998.

C.S. Revelle and K.E. Rosing, Defenders Imperium Romanum: a classical problem in military strategy, Amer.Math.Monthly, 107(7) (2000), 585-594.

Paul Andrew Dreyer, Jr, Dissertation Director: Fred S Roberts, Application and Variations of domination in graphs, New Brunswick, New Jersey, October 2000.

I. Stewart, Defend the Roman Empire!, Sci. Amer., 281 (6) (1999), 136-139.


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