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Dergiler / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2015 / Cilt: 11 Sayı: 2

Strong Domination Number of Some Graphs

Derya Doğan Durgun
Berna Lökçü
Sayfa
—
Yayın Tarihi
2015-12-19
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The strong domination number γ s of G is the minimum cardinality of an sd -set.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we consider strong domination number of P n k and C n k .
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Temel Bulgular & Veri:Let G=(V,E) be a graph, V is a vertex set and E is an edge set of graph G and u,v ∈V . u strongly dominates v and v weakly dominates u if (i) uv ∈ E and (ii) d ( u, G ) ≥ d ( v, G ) .
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Sonuç & Katkı:The strong domination number γ s of G is the minimum cardinality of an sd -set.
🔬Tür:Makale
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Domination Number · Strong Domination Number · Power of a Graph

Özet

In this paper, we consider strong domination number of P n k and C n k . Let G=(V,E) be a graph, V is a vertex set and E is an edge set of graph G and u,v ∈V . u strongly dominates v and v weakly dominates u if (i) uv ∈ E and (ii) d ( u, G ) ≥ d ( v, G ) . A set D ⊂V is a strong-dominating set ( sd -set) of G if every vertex in V-D is strongly dominated by at least one vertex in D . The strong domination number γ s of G is the minimum cardinality of an sd -set.

Abstract

In this paper, we consider strong domination number of P n k and C n k . Let G=(V,E) be a graph, V is a vertex set and E is an edge set of graph G and u,v ∈V . u strongly dominates v and v weakly dominates u if (i) uv ∈ E and (ii) d ( u, G ) ≥ d ( v, G ) . A set D ⊂V is a strong-dominating set ( sd -set) of G if every vertex in V-D is strongly dominated by at least one vertex in D . The strong domination number γ s of G is the minimum cardinality of an sd -set.

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Bu Makaleye Atıf Yap

Durgun, D. D. (2015). Strong Domination Number of Some Graphs. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 11 Sayı: 2. https://doi.org/10.18466/cbujos.21781

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Kaynakça (7)

  1. Barefoot, C.A.; Entringer, R.; Swart,H. Vulnerability in graphs a comparative survey, Journal of Combinatorial Mathematics and Combinational Computing. 1987; 1, 12-22.
  2. Haynes, T.W.; Hedetniemi, S.T.; Slater, P.J. Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  3. Haynes, T.W.; Hedetniemi, S.T.; Slater, P.J. (Eds.), Domination in Graphs, Advanced Topics, Marcel Dekker, New York, 1998.
  4. Sampathkumar, E.; Latha L. P. Strong weak domination and domination balance in a graph, Discrete Mathematics. 1996; 161(13), 235-242.
  5. Rautenbach, D. Bounds on the strong domination number, Discrete Mathematics. 2000; 215, pp. 201-212.
  6. Rautenbach, D. Bounds on the weak domination number, Australasian Journal of Combinatorics 18, 1998, pp.245-251.
  7. Domke G. S.; Hattingh J. H.; Markus L. R.; Ungerer E. On parameters related to strong and weak domination in graphs, Discrete Mathematics, 258, 2002, pp. 1-11.