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Keywords = triple octagonal chain

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Article
Total and Double Total Domination on Octagonal Grid
by Antoaneta Klobučar and Ana Klobučar Barišić
Axioms 2024, 13(11), 792; https://doi.org/10.3390/axioms13110792 - 16 Nov 2024
Cited by 2 | Viewed by 2948
Abstract
A k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set. The k-total domination number [...] Read more.
A k-total dominating set is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves, have at least k neighbors in the dominating set. The k-total domination number γkt(G) is the cardinality of the smallest k-total dominating set. For k=1,2, the k-total dominating number is called the total and the double total dominating number, respectively. In this paper, we determine the exact values for the total domination number on a linear and on a double octagonal chain and an upper bound for the total domination number on a triple octagonal chain. Furthermore, we determine the exact values for the double total domination number on a linear and on a double octagonal chain and an upper bound for the double total domination number on a triple octagonal chain and on an octagonal grid Om,n,m3,n3. As each vertex in the octagonal system is either of degree two or of degree three, there is no k-total domination for k3. Full article
(This article belongs to the Special Issue Recent Developments in Graph Theory)
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