Weakly convex and convex domination numbers for generalized Petersen and flower snark graphs

Kratica, Jozef; Matić, Dragan; Filipović, Vladimir

doi:10.33044/revuma.v61n2a16

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2020

2024

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Cited by 5 publications

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“…These graphs are denoted with J n and have 4n vertices and 6n edges, where vertex-set is Property 1. ( [15]) Let J n be a flower snark graph and j ∈ {0, 1, ..., n − 1} be an arbitrary number. Then the function h j : V (J n ) → V (J n ) defined as:…”

Section: Introductionmentioning

confidence: 99%

The mixed metric dimension of flower snarks and wheels

Danas¹

2020

Preprint

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New graph invariant, which is called mixed metric dimension, has been recently introduced. In this paper, exact results of mixed metric dimension on two special classes of graphs are found: flower snarks J n and wheels W n . It is proved that mixed metric dimension for J 5 is equal to 5, while for higher dimensions it is constant and equal to 4. For W n , its mixed metric dimension is not constant, but it is equal to n when n ≥ 4, while it is equal to 4, for n = 3.

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Section: Introductionmentioning

confidence: 99%

The mixed metric dimension of flower snarks and wheels

Danas¹

2020

Preprint

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“…Maksimovic et al (2018) [24],Kratica et al (2020)[21]) Consider the flower snark Jn, for n ≥ 3. Then we have γ R (Jn) = γwcon(Jn) = 2n, and γcon(Jn) = 4n.…”

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confidence: 99%

Variants of the Domination Number for Flower Snarks

Burdett,

Haythorpe,

Newcombe

2021

Preprint

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We consider the flower snarks, a widely studied infinite family of 3-regular graphs. For the Flower snark Jn on 4n vertices, it is trivial to show that the domination number of Jn is equal to n. However, results are more difficult to determine for variants of domination. The Roman domination, weakly convex domination, and convex domination numbers have been determined for flower snarks in previous works. We add to this literature by determining the independent domination, 2-domination, total domination, connected domination, upper domination, secure Domination and weak Roman domination numbers for flower snarks.

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