More results on the signed double Roman domination number of graphs
A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a neighbor w with [Formula: see text] or two neighbors...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2025-06-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2025.2511651 |
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| Summary: | A signed double Roman dominating function (SDRD-function) on a graph G is defined as a function [Formula: see text] having the property that [Formula: see text] for each [Formula: see text] and if [Formula: see text], then the vertex u must have a neighbor w with [Formula: see text] or two neighbors assigned 2 under f, and if [Formula: see text], then v must have at least one neighbor w with [Formula: see text]. The weight of an SDRD-function f is the value [Formula: see text]. The signed double Roman domination number[Formula: see text] is the minimum weight of an SDRD-function. It is conjectured that the signed double Roman domination number of a nontrivial graph G is bounded above by its order. In this paper we prove this conjecture for cactus graphs, and we present some new bounds on [Formula: see text]. We also determine the signed double Roman domination number of perfect binary trees. |
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| ISSN: | 0972-8600 2543-3474 |