• 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.
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