Minimum 2-Tuple Dominating Set of an Interval Graph

The -tuple domination problem, for a fixed positive integer , is to find a minimum size vertex subset such that every vertex in the graph is dominated by at least vertices in this set. The case when is called 2-tuple domination problem or double domination problem. In this paper, the 2-tuple domination problem is studied on interval graphs from an algorithmic point of view, which takes time, is the total number of vertices of the interval graph.

[1]  Gerard J. Chang,et al.  Algorithmic Aspects of Domination in Graphs , 1998 .

[2]  Frank Harary,et al.  Double Domination in Graphs , 2000, Ars Comb..

[3]  S. Hedetniemi,et al.  Domination in graphs : advanced topics , 1998 .

[4]  Teresa W. Haynes,et al.  Total Domination Edge Critical Graphs with Minimum Diameter , 2001, Ars Comb..

[5]  Madhumangal Pal,et al.  Interval Tree and its Applications 1 , 2009 .

[6]  Ronald D. Dutton,et al.  Vertex domination-critical graphs , 1988, Networks.

[7]  Madhumangal Pal,et al.  The Parallel Algorithms for Determining Edge-packing and Efficient Edge Dominating Sets in Interval Graphs , 1995, Parallel Algorithms Appl..

[8]  Madhumangal Pal,et al.  An optimal parallel algorithm for computing cut vertices and blocks on interval graphs , 2000, Int. J. Comput. Math..

[9]  Madhumangal Pal,et al.  An Optimal Algorithm to Solve 2-Neighbourhood Covering Problem on Interval Graphs , 2002, Int. J. Comput. Math..

[10]  Madhumangal Pal,et al.  A Data Structure on Interval Graphs and Its Applications , 1997, J. Circuits Syst. Comput..

[11]  Michael A. Henning,et al.  Domination in graphs , 1998 .

[12]  Gary MacGillivray,et al.  Domination critical graphs with higher independent domination numbers , 1996 .

[13]  Michael A. Henning,et al.  Graphs with large total domination number , 2000, J. Graph Theory.

[14]  C. P. Rangan,et al.  A Unified Approach to Domination Problems on Interval Graphs , 1988, Inf. Process. Lett..

[15]  Madhumangal Pal,et al.  An Algorithm to find a Minimum Feedback Vertex Set of an Interval Graph , 2005 .

[16]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[17]  Ewa Wojcicka.  Hamiltonian properties of domination-critical graphs , 1990, J. Graph Theory.

[18]  Gary MacGillivray,et al.  Vertex domination-critical graphs , 1995, Networks.

[19]  Madhumangal Pal,et al.  An Optimal Parallel Algorithm to Color an Interval Graph , 1996, Parallel Process. Lett..

[20]  Frank Harary,et al.  Nordhaus-Gaddum inequalities for domination in graphs , 1996, Discret. Math..

[21]  Peter J. Slater,et al.  Fundamentals of domination in graphs , 1998, Pure and applied mathematics.

[22]  Stephen T. Hedetniemi,et al.  Total domination in graphs , 1980, Networks.

[23]  Madhumangal Pal,et al.  Optimal sequential and parallel algorithms for computing the diameter and the center of an interval graph , 1995, Int. J. Comput. Math..