Sign Dominating Switched Invariants of a Graph
Abstract
In this paper, we newly constructed the sign dominating outer(inner) switched graph o d(G) (id(G)) of a graph G = (V;E) and establish their properties. Also we determine number of edges and its relation between o d(G) and i d(G) in some special classes of graphs are explored.
References
[1] B. D. Acharya. On characterizing graphs switching equivalent to acyclic graphs. Indian J. pure appl. Math., 12(10)(1981), 1187-1191.
[2] B. Zelinka. Signed and Minus domination in bipartite graphs. Czechoslovak Math. J., 56(2)(2006), 587-590.
[3] B. Chaluvaraju. 2-global and 2(i)-global dominating sets in graphs. Ultra scientist of Phy. Sc. - Section A: Mathematics, 20(2)(2008), 481-488.
[4] B. Chaluvaraju, C. Nandeesh Kumar and V. Chaitra, Special kind of colorable complements in Graphs, International J. Math. Combin., 3 (2013), 35-43.
[5] J.E. Dunbar, S.T. Hedetniemi, M.A. Henning, P.J. Slater. Signed domination in graphs. In: Y. Alavi, A. Schwenk (Eds.), Graph Theory, Combinatorics, and Algorithms, Proceedings
of the Seventh International Conference in Graph Theory, Combinatorics, Algorithms, and Applications, Kalamazoo, MI, 1992, (pp. 311-321). WileyInterscience, New York 1995.
[6] F. Harary. Graph theory. Addison-Wesley Publishing Company, MA, 1969.
[7] T. W. Haynes, S. T. Hedetniemi and P. J. Slater. Fundamental of Domination in Graphs. Marcel Dekker, Inc., New York 1998.
[8] V. R. Kulli, Theory of domination in graphs, Vishwa Internat. Publ., Gulbarga 2010.
[9] E. Sampathkumar and L. Pushpalatha. Complement of a graph: A generalization. Graphs and Combinatorics, 14(4)(1998), 377-392.
[10] E. Sampathkumar, L. Pushpalatha, C. V. Venkatachalam and Pradeep Bhat. Generalized Complements of a graph. Indian J. Pure Appl. Math., 29(6)(1998) 625-639.
[11] N. D. Soner, B. Janakiram and B. Chaluvaraju. Domination in 2-complement (2(i)-complement) of a graph. Adv. Stud. Contemp. Math., Kyungshang, 7(2)(2003), 145-154.
[12] J. H. Van-Lint and J. J. Seidel. Equilateral point sets in elliptic geometry. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences, 69(3)(1966), 335-348.
[13] L. Volmann and B. Zelinka. Signed domatic number of a graph. Discrete Appl. Math. 150(1-3)(2005), 261-267.
[2] B. Zelinka. Signed and Minus domination in bipartite graphs. Czechoslovak Math. J., 56(2)(2006), 587-590.
[3] B. Chaluvaraju. 2-global and 2(i)-global dominating sets in graphs. Ultra scientist of Phy. Sc. - Section A: Mathematics, 20(2)(2008), 481-488.
[4] B. Chaluvaraju, C. Nandeesh Kumar and V. Chaitra, Special kind of colorable complements in Graphs, International J. Math. Combin., 3 (2013), 35-43.
[5] J.E. Dunbar, S.T. Hedetniemi, M.A. Henning, P.J. Slater. Signed domination in graphs. In: Y. Alavi, A. Schwenk (Eds.), Graph Theory, Combinatorics, and Algorithms, Proceedings
of the Seventh International Conference in Graph Theory, Combinatorics, Algorithms, and Applications, Kalamazoo, MI, 1992, (pp. 311-321). WileyInterscience, New York 1995.
[6] F. Harary. Graph theory. Addison-Wesley Publishing Company, MA, 1969.
[7] T. W. Haynes, S. T. Hedetniemi and P. J. Slater. Fundamental of Domination in Graphs. Marcel Dekker, Inc., New York 1998.
[8] V. R. Kulli, Theory of domination in graphs, Vishwa Internat. Publ., Gulbarga 2010.
[9] E. Sampathkumar and L. Pushpalatha. Complement of a graph: A generalization. Graphs and Combinatorics, 14(4)(1998), 377-392.
[10] E. Sampathkumar, L. Pushpalatha, C. V. Venkatachalam and Pradeep Bhat. Generalized Complements of a graph. Indian J. Pure Appl. Math., 29(6)(1998) 625-639.
[11] N. D. Soner, B. Janakiram and B. Chaluvaraju. Domination in 2-complement (2(i)-complement) of a graph. Adv. Stud. Contemp. Math., Kyungshang, 7(2)(2003), 145-154.
[12] J. H. Van-Lint and J. J. Seidel. Equilateral point sets in elliptic geometry. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen: Series A: Mathematical Sciences, 69(3)(1966), 335-348.
[13] L. Volmann and B. Zelinka. Signed domatic number of a graph. Discrete Appl. Math. 150(1-3)(2005), 261-267.
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2016-12-31
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