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## Discussiones Mathematicae Graph Theory

2001 | 21 | 1 | 119-136
Tytuł artykułu

### Odd and residue domination numbers of a graph

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
119-136
Opis fizyczny
Daty
wydano
2001
otrzymano
2000-10-30
poprawiono
2001-01-17
Twórcy
autor
• Department of Mathematics, University of Haifa - Oranim, Tivon - 36006, Israel
• Deptartment of Computer and Information Sciences, University of North Florida, Jacksonville, FL 32224, USA
autor
• Department of Mathematics, West Virginia University, Morgantown, WV 26506
Bibliografia
• [1] A. Amin, L. Clark, and P. Slater, Parity Dimension for Graphs, Discrete Math. 187 (1998) 1-17, doi: 10.1016/S0012-365X(97)00242-2.
• [2] A. Amin and P. Slater, Neighborhood Domination with Parity Restriction in Graphs, Congr. Numer. 91 (1992) 19-30.
• [3] A. Amin and P. Slater, All Parity Realizable Trees, J. Comb. Math. Comb. Comput. 20 (1996) 53-63.
• [4] Y. Caro, Simple Proofs to Three Parity Theorems, Ars Combin. 42 (1996) 175-180.
• [5] Y. Caro and W. Klostermeyer, The Odd Domination Number of a Graph, J. Comb. Math. Comb. Comput. (2000), to appear.
• [6] E. Cockayne, E. Hare, S. Hedetniemi and T. Wimer, Bounds for the Domination Number of Grid Graphs, Congr. Numer. 47 (1985) 217-228.
• [7] M. Garey and D. Johnson, Computers and Intractability (W.H. Freeman, San Francisco, 1979).
• [8] J. Goldwasser, W. Klostermeyer, G. Trapp and C.-Q. Zhang, Setting Switches on a Grid, Technical Report TR-95-20, Dept. of Statistics and Computer Science (West Virginia University, 1995).
• [9] J. Goldwasser, W. Klostermeyer and G. Trapp, Characterizing Switch-Setting Problems, Linear and Multilinear Algebra 43 (1997) 121-135, doi: 10.1080/03081089708818520.
• [10] J. Goldwasser and W. Klostermeyer, Maximization Versions of Lights Out'' Games in Grids and Graphs, Congr. Numer. 126 (1997) 99-111.
• [11] J. Goldwasser, W. Klostermeyer and H. Ware, Fibonacci Polynomials and Parity Domination in Grid Graphs, Graphs and Combinatorics (2000), to appear.
• [12] M. Halldorsson, J. Kratochvil and J. Telle, Mod-2 Independence and Domination in Graphs, in: Proceedings Workshop on Graph-Theoretic Concepts in Computer Science '99, Ascona, Switzerland (Springer-Verlag, Lecture Notes in Computer Science, 1999).
• [13] T. Haynes, S. Hedetniemi and P. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
• [14] R. Johnson and C. Johnson, Matrix Analysis (Cambridge University Press, 1990).
• [15] M. Jacobson and L. Kinch, On the Domination Number of Products of Graphs, Ars Combin. 18 (1984) 33-44.
• [16] W. Klostermeyer and E. Eschen, Perfect Codes and Independent Dominating Sets, Congr. Numer. (2000), to appear.
• [17] K. Sutner, Linear Cellular Automata and the Garden-of-Eden, The Mathematical Intelligencer 11 (2) (1989) 49-53.
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Bibliografia
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