An upper bound on the double domination number of trees

Amjadi, Jafar

doi:10.5937/kgjmath1502133a

Cited by 6 publications

(3 citation statements)

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“…The relation between the annihilation number and various parameters of a graph were studied in [1,2,7,8,9,11,13,18,31].…”

Section: Lemma 11 Every Independent Vertex Cover Of a Graph Without I...mentioning

confidence: 99%

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On an Annihilation Number Conjecture

Levit¹,

Mândrescu²

2018

Preprint

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Let α(G) denote the cardinality of a maximum independent set, while µ(G) be the size of a maximum matching in the grapha∈A deg(a) ≤ |E| is an annihilation set; if, in addition, deg (v) + a∈A deg(a) > |E|, for every vertex v ∈ V (G) − A, then A is a maximal annihilation set in G.In [23] it was conjectured that the following assertions are equivalent:(ii) G is a König-Egerváry graph and every maximum independent set is a maximal annihilating set.In this paper, we prove that the implication "(i) =⇒ (ii)" is correct, while for the opposite direction we provide a series of generic counterexamples.

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“…The relation between the annihilation number and various parameters of a graph were studied in [1,2,7,8,9,11,13,18,31].…”

Section: Lemma 11 Every Independent Vertex Cover Of a Graph Without I...mentioning

confidence: 99%

“…Let D =(1,2,3,4,4). For Θ = 3, we get h (D, Θ) = 2 and A = (1, 2) is a maximum subsequence of D. For Θ = 6, we get h (D, Θ) = 3 and A 1 = (1, 2, 3) is a maximum subsequence of D, while A 2 = (2, 4) is a maximal non-maximum subsequence of D.…”

mentioning

confidence: 99%

On an Annihilation Number Conjecture

Levit¹,

Mândrescu²

2018

Preprint

View full text Add to dashboard Cite

show abstract

“…The relation between the annihilation number and various parameters of a graph were studied in [1,2,7,8,9,10,12,14,15,19,32,33].…”

Section: Introductionmentioning

confidence: 99%

On an annihilation number conjecture

Levit

Mândrescu

2020

Ars Math. Contemp.

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Let α(G) denote the cardinality of a maximum independent set, while µ(G) be the size of a maximum matching in the graphIn 2011, Larson and Pepper conjectured that the following assertions are equivalent:(ii) G is a König-Egerváry graph and every maximum independent set is a maximal annihilating set.It turns out that the implication "(i) =⇒ (ii)" is correct.In this paper, we show that the opposite direction is not valid, by providing a series of generic counterexamples.

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