On Locating-Dominating Set of Regular Graphs
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Let G be a simple, connected, and finite graph. For every vertex v ∈ V G , we denote by N G v the set of neighbours of v in G . The locating-dominating number of a graph G is defined as the minimum cardinality of W ⊆ V G such that every two distinct vertices u , v ∈ V G \ W satisfies ∅ ≠ N G u ∩ W ≠ N G v ∩ 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 .
2020 ◽
Vol 2
(2)
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pp. 105-110
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2020 ◽
Vol 8
(5)
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pp. 4579-4583
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2015 ◽
Vol 23
(2)
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pp. 187-199
2019 ◽
Vol 11
(01)
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pp. 1950004