On Locating-Dominating Set of Regular Graphs
Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8147514 |
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| Summary: | Let G be a simple, connected, and finite graph. For every vertex v∈VG, we denote by NGv the set of neighbours of v in G. The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ VG such that every two distinct vertices u,v∈VG\W satisfies ∅≠NGu∩W≠NGv∩W≠∅. A graph G is called k-regular graph if every vertex of G is adjacent to k other vertices of G. In this paper, we determine the locating-dominating number of k-regular graph of order n, where k=n−2 or k=n−3. |
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| ISSN: | 2314-4629 2314-4785 |