The Slater and Sub-k-Domination Number of a Graph with Applications to Domination and k-Domination
In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp l...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Sciendo
2020-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2134 |
| Summary: | In this paper we introduce and study a new graph invariant derived from the degree sequence of a graph G, called the sub-k-domination number and denoted subk(G). This invariant serves as a generalization of the Slater number; in particular, we show that subk(G) is a computationally efficient sharp lower bound on the k-domination number of G, and improves on several known lower bounds. We also characterize the sub-k-domination numbers of several families of graphs, provide structural results on sub-k-domination, and explore properties of graphs which are subk(G)-critical with respect to addition and deletion of vertices and edges. |
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| ISSN: | 2083-5892 |