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Minimal Roman Dominating Function

Authors: Sanket Mukundbhai Badiyani; D. K. Thakkar;

Minimal Roman Dominating Function

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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