2022
DOI: 10.48550/arxiv.2204.07040
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Total domination number of middle graphs

Abstract: A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. In this paper, we study the total domination number of middle graphs. Indeed, we obtain tight bounds for this number in terms of the order of the graph G. We also compute the total domination number of the middle graph of some known families of graphs explicitly. Moreove… Show more

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“…A total dominating set of 𝐺 is defined as a dominating set 𝑆 in which the induced subgraph ⟨𝑆⟩ has no isolated vertex [8,9]. It is implied that every vertex in 𝑆 has atleast one adjacent vertex in 𝑆, which means that all the vertex in 𝑆 are connected.…”
Section: Introductionmentioning
confidence: 99%
“…A total dominating set of 𝐺 is defined as a dominating set 𝑆 in which the induced subgraph ⟨𝑆⟩ has no isolated vertex [8,9]. It is implied that every vertex in 𝑆 has atleast one adjacent vertex in 𝑆, which means that all the vertex in 𝑆 are connected.…”
Section: Introductionmentioning
confidence: 99%