Murat Erşen BERBERLER, Zeynep Nihan BERBERLER

Independence Saturation In Complementary Product Types of Graphs

The independence saturation number IS (G) of graph (V, E) is defined as min {IS (u) V} where IS (u) is the maximum cardinality of an independent set that contains vertex Let G— be the complement graph of Complementary prisms are the subset of complementary product graphs. The complementary prism of is the graph formed from the disjoint union of and G— by adding the edges of perfect matching between the corresponding vertices of and In this paper, the independence saturation in complementary prisms are considered, then the complementary prisms with small independence saturation numbers are characterized.

PDF

___

[1] Korshunov, A.D. Coefficient of Internal Stability of Graphs. Cybernetics. 1974; 10, 19-33.
[2] Bomze, I.; Budinich, M.; Pardalos, P.; Pelillo, M. The Maximum Clique Problem. Handbook of Combinatorial Optimization, Supplement Volume A; Du, D., Pardalos, P., Eds. Kluwer Academic Press: 1999.
[3] Subramanian, M. Studies in Graph TheoryIndependence Saturation in Graphs, PhD thesis, Manonmaniam Sundaranar University, 2004.
[4] West, D.B. Introduction to Graph Theory; Prentice Hall, NJ, 2001.
[5] Buckley, F.; Harary, F. Distance in Graphs; AddisonWesley Publishing Company Advanced Book Program, Redwood City, CA, 1990.
[6] Haynes, T.W.; Henning, M.A.; Slater, P.J.; Merwe, V.D. The Complementary Product of Two Graphs. Bulletinof the Institute of Combinatorics and its Applications. 2007; 51, 331 CBU J. of Sci., Volume 13, Issue 2, 325-331 21-30.
[7] Arumugam, S.; Subramanian, M. Independence Saturation and Extended Domination Chain in graphs. AKCE International Journal of Graphs and Combinatorics. 2007; 4, 59-69.
[8] Gongora, J.A.; Haynes, T.W.; Jum, E. Independent Domination in Complementary Prisms. Utilitas Mathematica. 2013; 91, 3-12.
[9] Aytaç, A.; Turacı, T. Strong Weak Domination in Complementary Prisms. Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications Algorithms. 2015; 22(2b), 85-96.
[10] Gölpek, T.H.; Turacı, T.; Coskun, B. On The Average Lower Domination Number and Some Results of Complementary Prisms and Graph Join. Journal of Advanced Research in Applied Mathematics. 2015; 7(1), 52-61.
[11] Desormeaux, W.J.; Haynes, T.W.; Vaughan, L. Double Domination in Complementray Prisms. Utilitas Mathematica. 2013; 91, 131-142.
[12] Desormeaux, W.J.; Haynes, T.W. Restrained Domination in Complementray Prisms. Utilitas Mathematica. 2011; 86, 267-278.
[13] Kazemi, A.P. k-Tuple Total Restrained Domination in Complementary Prisms. ISRN Combinatorics. 2013; doi:10.1155/2013/984549.
[14] Chaluvaraju, B.; Chaitra, V. Roman domination in Complementary Prism Graphs. International Journal of Mathematical Combinatorics. 2012; 2, 24-31
[15] Muthulakshmi, T.; Subramanian, M. Independence saturation number of some classes of graphs. Far East Journal of Mathematical Sciences. 2014; 86(1), 11-21.
[16] Berberler, Z.N.; Berberler, M.E. Independently Saturated Graphs. TWMS Journal of Applied and Engineering Mathematics. Accepted. 2017.
[17] Haynes, T.W.; Henning, M.A.; Merwe, V.D. Domination and total domination in complementary prisms. Journal of Combinatorial Optimzation. 2009; 18, 23-37.
[18] Holmes, K.R.S.; Koessler, D.R.; Haynes, T.W. Locatingdomination in complementary prisms. Journal of Combinatorial Mathematics and Combinatorial Computing. 2010; 72, 163-171.

Celal Bayar Üniversitesi Fen Bilimleri Dergisi-Cover

ISSN: 1305-130X
Başlangıç: 2005
Yayıncı: Manisa Celal Bayar Üniversitesi Fen Bilimleri Enstitüsü

Arşiv