Strong Domination Number of Some Graphs
Strong Domination Number of Some Graphs

Derya Doğan Durgun [1] , Berna Lökçü [2]

353 754

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.

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.

 

  • 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.
Primary Language EN
Journal Section Articles
Authors

Author: Derya Doğan Durgun

Author: Berna Lökçü

Dates

Publication Date: December 19, 2015

Bibtex @ { cbayarfbe238121, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {Celal Bayar University}, year = {2015}, volume = {11}, pages = {0 - }, doi = {10.18466/cbujos.21781}, title = {Strong Domination Number of Some Graphs}, key = {cite}, author = {Doğan Durgun, Derya and Lökçü, Berna} }
APA Doğan Durgun, D , Lökçü, B . (2015). Strong Domination Number of Some Graphs. Celal Bayar University Journal of Science, 11 (2), . Retrieved from http://dergipark.org.tr/cbayarfbe/issue/22163/238121
MLA Doğan Durgun, D , Lökçü, B . "Strong Domination Number of Some Graphs". Celal Bayar University Journal of Science 11 (2015): <http://dergipark.org.tr/cbayarfbe/issue/22163/238121>
Chicago Doğan Durgun, D , Lökçü, B . "Strong Domination Number of Some Graphs". Celal Bayar University Journal of Science 11 (2015):
RIS TY - JOUR T1 - Strong Domination Number of Some Graphs AU - Derya Doğan Durgun , Berna Lökçü Y1 - 2015 PY - 2015 N1 - DO - T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 0 EP - VL - 11 IS - 2 SN - 1305-130X-1305-1385 M3 - UR - Y2 - 2019 ER -
EndNote %0 Celal Bayar University Journal of Science Strong Domination Number of Some Graphs %A Derya Doğan Durgun , Berna Lökçü %T Strong Domination Number of Some Graphs %D 2015 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 11 %N 2 %R %U
ISNAD Doğan Durgun, Derya , Lökçü, Berna . "Strong Domination Number of Some Graphs". Celal Bayar University Journal of Science 11 / 2 (December 2015): 0-.
AMA Doğan Durgun D , Lökçü B . Strong Domination Number of Some Graphs. Celal Bayar Univ J Sci. 2015; 11(2): 0-.
Vancouver Doğan Durgun D , Lökçü B . Strong Domination Number of Some Graphs. Celal Bayar University Journal of Science. 2015; 11(2): -0.