Further results on outer independent triple Roman domination
An outer-independent triple Roman dominating function (OI[3]RDF) on a graph [Formula: see text] is function [Formula: see text] having the property that (i) if [Formula: see text] then v must have either a neighbor assigned 4 or two neighbors one of which is assigned 3 and the other at least 2 or v...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2025-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2421988 |
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| Summary: | An outer-independent triple Roman dominating function (OI[3]RDF) on a graph [Formula: see text] is function [Formula: see text] having the property that (i) if [Formula: see text] then v must have either a neighbor assigned 4 or two neighbors one of which is assigned 3 and the other at least 2 or v has three neighbors all assigned 2; (ii) no two vertices assigned 0 are adjacent; (iii) if [Formula: see text], then v must have either a neighbor assigned at least 3 or two neighbors assigned 2; (iv) if [Formula: see text], then v must have one neighbor assigned at least 2. The weight of an OI[3]RDF is the sum of its function value over the whole set of vertices, and the outer-independent triple Roman domination number of G is the minimum weight of an OI[3]RDF on G. In this paper, we continue the study of outer-independent triple Roman domination number in graphs. First, we characterize all graphs with small or large outer-independent triple Roman domination number, and then we establish relationships with some other related parameters. Finally we present a sharp upper bound for the outer-independent triple Roman domination number of trees. |
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| ISSN: | 0972-8600 2543-3474 |