Effect of vertex deletion on the weak Roman domination number of a graph
Let be a graph and be a function. The weight of a vertex is and a vertex with weight is said to be undefended with respect to , if it is not adjacent to a vertex with positive weight. The function is a weak Roman dominating function (WRDF) if each vertex with is adjacent to a vertex with such that t...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2019-08-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1016/j.akcej.2017.12.003 |
| Summary: | Let be a graph and be a function. The weight of a vertex is and a vertex with weight is said to be undefended with respect to , if it is not adjacent to a vertex with positive weight. The function is a weak Roman dominating function (WRDF) if each vertex with is adjacent to a vertex with such that the function defined by , and if , has no undefended vertex. The weight of is . The weak Roman domination number, denoted by , is the minimum weight of a weak Roman dominating function on . In this paper we examine the effects on when is modified by deleting a vertex. |
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| ISSN: | 0972-8600 |