Cartesian product graphs and k-tuple total domination

Kazemi, P Adel; Pahlavsay, Behnaz; Stones, J Rebecca

doi:10.2298/fil1819713k

Cited by 6 publications

(6 citation statements)

References 12 publications

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“…We first remark the following Vizing-like inequality for the packing number proved by Kazemi et al [17]. That is, for all graphs G and H, ρ(G H) ≥ ρ(G)ρ(H).…”

Section: Cartesian Product Of Graphsmentioning

confidence: 88%

(Open) packing number of some graph products

Mojdeh,

Peterin,

Samadi

et al. 2019

Preprint

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The packing number of a graph G is the maximum number of closed neighborhoods of vertices in G with pairwise empty intersections. Similarly, the open packing number of G is the maximum number of open neighborhoods in G with pairwise empty intersections. We consider the packing and open packing numbers on graph products. In particular we give a complete solution with respect to some properties of factors in the case of lexicographic and rooted products. For Cartesian, strong and direct products, we present several lower and upper bounds on these parameters.

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“…We first remark the following Vizing-like inequality for the packing number proved by Kazemi et al [17]. That is, for all graphs G and H, ρ(G H) ≥ ρ(G)ρ(H).…”

Section: Cartesian Product Of Graphsmentioning

confidence: 88%

(Open) packing number of some graph products

Mojdeh,

Peterin,

Samadi

et al. 2019

Preprint

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“…The double total domination number has been well studied by the research community. For instance, in [1,4,17,19,21,22], some combinatorial results were presented, and in [2,3,18,23], some studies on certain product graphs were carried out. Our goal is to making some new remarkable contributions to this domination parameter.…”

Section: Introductionmentioning

confidence: 99%

New Bounds on the Double Total Domination Number of Graphs

Martínez

Hernández-Mira

2021

Bull. Malays. Math. Sci. Soc.

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Let G be a graph of minimum degree at least two. A set $$D\subseteq V(G)$$ D ⊆ V ( G ) is said to be a double total dominating set of G if $$|N(v)\cap D|\ge 2$$ | N ( v ) ∩ D | ≥ 2 for every vertex $$v\in V(G)$$ v ∈ V ( G ) . The minimum cardinality among all double total dominating sets of G is the double total domination number of G. In this article, we continue with the study of this parameter. In particular, we provide new bounds on the double total domination number in terms of other domination parameters. Some of our results are tight bounds that improve some well-known results.

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“…In [9] it was shown that the domination number can be also bounded from above by the packing number multiplied by the maximum degree of a graph. The inequality for the packing number of Vizing conjecture type was proven in [13].…”

Section: Introductionmentioning

confidence: 99%

Graphs with unique maximum packing of closed neighborhoods

Božović¹,

Peterin²

2020

Discuss. Math. Graph Theory

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A packing of a graph G is a subset P of the vertex set of G such that the closed neighborhoods of any two distinct vertices of P do not intersect. We study graphs with a unique packing of the maximum cardinality. We present several general properties for such graphs. These properties are used to characterize the trees with a unique maximum packing. Two characterizations are presented where one of them is inductive based on five operations.

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Cartesian product graphs and k-tuple total domination

Cited by 6 publications

References 12 publications

(Open) packing number of some graph products

(Open) packing number of some graph products

New Bounds on the Double Total Domination Number of Graphs

Graphs with unique maximum packing of closed neighborhoods

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