Signed total double Roman dominating functions in graphs
A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, (ii) every vertex v with f(v)...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2024-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2357561 |
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| Summary: | A signed total double Roman dominating function (STDRDF) on an isolated-free graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex v with [Formula: see text] has at least two neighbors assigned 2 under f or one neighbor w with f(w) = 3, (ii) every vertex v with f(v) = 1 has at least one neighbor w with [Formula: see text] and (iii) [Formula: see text] holds for any vertex v. The weight of a STDRDF is the value [Formula: see text] The signed total double Roman domination number [Formula: see text] is the minimum weight of a STDRDF on G. In this article, we provide various bounds on [Formula: see text] and we show that the corresponding decision problem is NP-complete for bipartite and chordal graphs. In addition, we determine the signed total double Roman domination number of some classes of graphs including cycles, complete graphs and complete bipartite graphs. |
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| ISSN: | 0972-8600 2543-3474 |