Total Roman {2}-Dominating Functions in Graphs
A Roman {2}-dominating function (R2F) is a function : → {0, 1, 2} with the property that for every vertex ∈ with ) = 0 there is a neighbor of with ) = 2, or there are two neighbors of with ) = ) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F such that the set of vertices with ) 0 induc...
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| Veröffentlicht in: | Discussiones Mathematicae. Graph Theory 2022-08, Vol.42 (3), p.937-958 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A Roman {2}-dominating function (R2F) is a function
:
→ {0, 1, 2} with the property that for every vertex
∈
with
) = 0 there is a neighbor
of
with
) = 2, or there are two neighbors
of
with
) =
) = 1. A total Roman {2}-dominating function (TR2DF) is an R2F
such that the set of vertices with
)
0 induce a subgraph with no isolated vertices. The weight of a TR2DF is the sum of its function values over all vertices, and the minimum weight of a TR2DF of
is the total Roman {2}-domination number
). In this paper, we initiate the study of total Roman {2}-dominating functions, where properties are established. Moreover, we present various bounds on the total Roman {2}-domination number. We also show that the decision problem associated with
) is possible to compute this parameter in linear time for bounded clique-width graphs (including trees). |
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| ISSN: | 1234-3099 2083-5892 |
| DOI: | 10.7151/dmgt.2316 |