Sanket Mukundbhai Badiyani, D K Thakkar


In this paper we introduce a new concepts namely Roman Free Functions, Maximal Roman Free Functions, Roman Free Number and others. Every Maximal Roman Free Function is a Roman Dominating Function. A Minimal Roman Dominating Function need not be a Maximal Roman Free Function. We also give an example of a Maximal Roman Free Function which is not a Minimal Roman Dominating Function. In addition to this we prove that the minimum weight of a Maximal Roman Free Function of a Roman Graph is the Roman Domination Number of the graph.

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