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https://hdl.handle.net/1959.11/23484
Title: | On the Power Domination Number of de Bruijn and Kautz Digraphs | Contributor(s): | Grigorious, Cyriac (author); Kalinowski, Thomas (author) ; Stephen, Sudeep (author) | Publication Date: | 2018 | Open Access: | Yes | DOI: | 10.1007/978-3-319-78825-8_22 | Handle Link: | https://hdl.handle.net/1959.11/23484 | Open Access Link: | https://arxiv.org/abs/1612.01721 | Abstract: | Let G=(V,A) be a directed graph, and let S⊆V be a set of vertices. Let the sequence S=S₀⊆S₁⊆S₂⊆⋯ be defined as follows: S₁ is obtained from S₀ by adding all out-neighbors of vertices in S₀. For k⩾2, Sₖ is obtained from Sₖ₋₁ by adding all vertices w such that for some vertex v∈Sₖ₋₁, w is the unique out-neighbor of v in V∖Sₖ₋₁. We set M(S)=S₀∪S₁∪⋯, and call S a power dominating set for G if M(S)=V(G). The minimum cardinality of such a set is called the power domination number of G. In this paper, we determine the power domination numbers of de Bruijn and Kautz digraphs. | Publication Type: | Conference Publication | Conference Details: | IWOCA 2017: 28th International Workshop on Combinatorial Algorithms, Newcastle, Australia, 17th - 21st July, 2017 | Source of Publication: | Combinatorial Algorithms, v.10765, p. 264-272 | Publisher: | Springer | Place of Publication: | Cham, Switzerland | Fields of Research (FoR) 2008: | 010104 Combinatorics and Discrete Mathematics (excl. Physical Combinatorics) | Fields of Research (FoR) 2020: | 490404 Combinatorics and discrete mathematics (excl. physical combinatorics) | Socio-Economic Objective (SEO) 2008: | 970101 Expanding Knowledge in the Mathematical Sciences | Socio-Economic Objective (SEO) 2020: | 280118 Expanding knowledge in the mathematical sciences | Peer Reviewed: | Yes | HERDC Category Description: | E1 Refereed Scholarly Conference Publication | Series Name: | Lecture Notes in Computer Science |
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Appears in Collections: | Conference Publication School of Science and Technology |
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