Minimal Roman dominating function

D. K Thakkar, Sanket Mukundbhai Badiyani

Abstract


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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References


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