Further results on independent double roman trees
AbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2148140 |
| Summary: | AbstractA double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that every vertex u with f(u) = 0 is adjacent to at least one vertex assigned a 3 or to at least two vertices assigned a 2, and every vertex v with f(v) = 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a DRDF is the sum of its function values over all vertices. A DRDF f is an independent double Roman dominating function (IDRDF) if the set of vertices assigned 1, 2 and 3 is independent. The independent double Roman domination number [Formula: see text] is the minimum weight over all IDRDFs of G. Every graph G satisfies [Formula: see text] where i(G) is the independent domination number. In this paper, we give a characterization of all trees T with [Formula: see text] |
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| ISSN: | 0972-8600 2543-3474 |