• ON THE ROMAN DOMINATION NUMBER OF GRAPHS
Abstract
In this manuscript we consider the change in the Roman Domination Number of a graph when a vertex is removed from the graph. We prove a necessary and sufficient condition under which the Roman Domination Number of a graph increases. Also we prove a necessary and sufficient condition under which the Roman Domination Number decreases. We deduce that in any graph there are vertices whose removal does not increase the Roman Domination Number.
Keywords
Roman Dominating Function, Roman Domination Number, Minimal Roman Dominating Function, Minimum Roman Dominating Function, Private Neighbourhood.
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