Two relations between the parameters of independence and irredundance
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It is shown that i + IR⩽2n + 2δ − 2 2nδ , which was conjectured by Cockayne, Favaron, Payan and Thomason, and that i = i + 2 δIR ⩽n + δ .About:
This article is published in Discrete Mathematics.The article was published on 1988-06-01 and is currently open access. It has received 44 citations till now. The article focuses on the topics: Maximal independent set & Frequency partition of a graph.read more
Citations
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Independent domination in graphs: A survey and recent results
Wayne Goddard,Michael A. Henning +1 more
TL;DR: A survey of selected recent results on independent domination in graphs is offered and it is shown that not every vertex in S is adjacent to a vertex in S .
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On the Independent Domination Number of Regular Graphs
TL;DR: A set S of vertices in a graph G is an independent dominating set of G if and only if every vertex not in S is adjacent to a vertex in S as mentioned in this paper.
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On independent domination number of regular graphs
TL;DR: This paper settles the conjecture of Haviland in the negative by constructing counterexamples, and shows that a connected cubic graph G of order n ⩾ 8 satisfies i ( G ) ⩽ 2 n /5, providing a new upper bound for cubic graphs.
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Independent domination in regular graphs
TL;DR: This work investigates the maximum value of the product of the independent domination numbers of a graph and its complement, as a function of n, and proves that if G is regular then i(G) · i( G ) 2 /12.68 .
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Breaking the 2n-barrier for Irredundance: Two lines of attack
Daniel Binkele-Raible,Ljiljana Brankovic,Marek Cygan,Henning Fernau,Joachim Kneis,Dieter Kratsch,Alexander Langer,Mathieu Liedloff,Marcin Pilipczuk,Peter Rossmanith,Jakub Onufry Wojtaszczyk +10 more
TL;DR: In this paper, exact exponential-time algorithms for computing the lower and upper irredundance numbers of a graph G on n vertices with running time O(1.99914^n) and O( 1.9369^n, respectively, were presented.
References
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Graph‐theoretic parameters concerning domination, independence, and irredundance
Béla Bollobás,Ernest J. Cockayne +1 more
TL;DR: It is proved that for any graph G, ir (G) > γ(G)/2 and for any grpah G with p vertices and no isolated vertices, i(G) ≤ p-γ(G), which is the minimum cardinality taken over all maximal sets of vertices having no redundancies.
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Contributions to the theory of domination, independence and irredundance in graphs
TL;DR: A conjecture of Hoyler and Cockayne [9], namely i+@b=<2p + 2@d - 22p@d, is proved and sufficient conditions for the equality of the three upper parameters are given.
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On the sum of two parameters concerning independence and irredundance in a graph
TL;DR: This paper proves that i(G) + IR (G) ⩽ 2p + 2k − 2√2 2pk was proposed in [1], where p = | G | and k is the minimum degree of G .