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Strong Domination Number of Some Graphs

Year 2015, Volume: 11 Issue: 2, 0 - , 19.12.2015

Derya Doğan Durgun , Berna Lökçü

Abstract

In this paper, we consider strong domination number of Pnk  and Cnk .  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 γs of G is the minimum cardinality of an sd-set.

Keywords

Domination Number Strong Domination Number Power of a Graph Networks sd-set

References

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

Strong Domination Number of Some Graphs

Year 2015, Volume: 11 Issue: 2, 0 - , 19.12.2015

Derya Doğan Durgun , Berna Lökçü

Abstract

In this paper, we consider strong domination number of Pnk  and Cnk .  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 γs of G is the minimum cardinality of an sd-set.

 

Keywords

Domination Number Strong Domination Number Power of a Graph Networks sd-set

References

  • Barefoot, C.A.; Entringer, R.; Swart,H. Vulnerability in graphs a comparative survey, Journal of Combinatorial Mathematics and Combinational Computing. 1987; 1, 12-22.
  • Haynes, T.W.; Hedetniemi, S.T.; Slater, P.J. Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  • Haynes, T.W.; Hedetniemi, S.T.; Slater, P.J. (Eds.), Domination in Graphs, Advanced Topics, Marcel Dekker, New York, 1998.
  • Sampathkumar, E.; Latha L. P. Strong weak domination and domination balance in a graph, Discrete Mathematics. 1996; 161(13), 235-242.
  • Rautenbach, D. Bounds on the strong domination number, Discrete Mathematics. 2000; 215, pp. 201-212.
  • Rautenbach, D. Bounds on the weak domination number, Australasian Journal of Combinatorics 18, 1998, pp.245-251.
  • 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.
There are 7 citations in total.

Details

Primary Language EN
Journal Section Articles
Authors

Derya Doğan Durgun

Berna Lökçü This is me

Publication Date December 19, 2015
Published in Issue Year 2015 Volume: 11 Issue: 2

Cite

APA Doğan Durgun, D., & Lökçü, B. (2015). Strong Domination Number of Some Graphs. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, 11(2). https://doi.org/10.18466/cbujos.21781
AMA Doğan Durgun D, Lökçü B. Strong Domination Number of Some Graphs. CBUJOS. December 2015;11(2). doi:10.18466/cbujos.21781
Chicago Doğan Durgun, Derya, and Berna Lökçü. “Strong Domination Number of Some Graphs”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 11, no. 2 (December 2015). https://doi.org/10.18466/cbujos.21781.
EndNote Doğan Durgun D, Lökçü B (December 1, 2015) Strong Domination Number of Some Graphs. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 11 2
IEEE D. Doğan Durgun and B. Lökçü, “Strong Domination Number of Some Graphs”, CBUJOS, vol. 11, no. 2, 2015, doi: 10.18466/cbujos.21781.
ISNAD Doğan Durgun, Derya - Lökçü, Berna. “Strong Domination Number of Some Graphs”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi 11/2 (December 2015). https://doi.org/10.18466/cbujos.21781.
JAMA Doğan Durgun D, Lökçü B. Strong Domination Number of Some Graphs. CBUJOS. 2015;11. doi:10.18466/cbujos.21781.
MLA Doğan Durgun, Derya and Berna Lökçü. “Strong Domination Number of Some Graphs”. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, vol. 11, no. 2, 2015, doi:10.18466/cbujos.21781.
Vancouver Doğan Durgun D, Lökçü B. Strong Domination Number of Some Graphs. CBUJOS. 2015;11(2).