The strong domination problem in block graphs and proper interval graphs

In a graph G = (V,E), the degree of a vertex v ∈ V, denoted by dG(v), is defined as the number of edges incident on v. A set D of vertices of G is called a strong dominating set if for every v ∈ V ...

[1]  Gerard J. Chang,et al.  On the mixed domination problem in graphs , 2013, Theor. Comput. Sci..

[2]  Giorgio Gambosi,et al.  Complexity and Approximation , 1999, Springer Berlin Heidelberg.

[3]  Viggo Kann,et al.  Hardness of Approximating Problems on Cubic Graphs , 1997, CIAC.

[4]  E. Sampathkumar,et al.  Strong weak domination and domination balance in a graph , 1996, Discret. Math..

[5]  Mihalis Yannakakis,et al.  Edge Dominating Sets in Graphs , 1980 .

[6]  Xuding Zhu,et al.  Rainbow domination on trees , 2010, Discret. Appl. Math..

[7]  Dieter Rautenbach.  Bounds on the strong domination number , 2000, Discret. Math..

[8]  Stephen T. Hedetniemi,et al.  A Linear Algorithm for the Domination Number of a Tree , 1975, Inf. Process. Lett..

[9]  Vasek Chvátal,et al.  A Greedy Heuristic for the Set-Covering Problem , 1979, Math. Oper. Res..

[10]  G. Nemhauser,et al.  The k-Domination and k-Stability Problems on Sun-Free Chordal Graphs , 1984 .

[11]  Dieter Rautenbach,et al.  Perfect graphs of strong domination and independent strong domination , 2001, Discret. Math..

[12]  Bhawani Sankar Panda,et al.  A linear time recognition algorithm for proper interval graphs , 2003, Inf. Process. Lett..

[13]  Gerard J. Chang,et al.  Algorithmic aspects of the kk-domination problem in graphs , 2013, Discret. Appl. Math..

[14]  Stephen T. Hedetniemi,et al.  A linear algorithm for finding a minimum dominating set in a cactus , 1986, Discret. Appl. Math..

[15]  S. M. Hedetniemi,et al.  On the Algorithmic Complexity of Total Domination , 1984 .

[16]  Yancai Zhao,et al.  The algorithmic complexity of mixed domination in graphs , 2011, Theor. Comput. Sci..

[17]  Kellogg S. Booth,et al.  Dominating Sets in Chordal Graphs , 1982, SIAM J. Comput..

[18]  Miroslav Chlebík,et al.  Approximation hardness of dominating set problems in bounded degree graphs , 2008, Inf. Comput..

[19]  Dieter Rautenbach.  The influence of special vertices on strong domination , 1999 .

[20]  Johannes H. Hattingh,et al.  On parameters related to strong and weak domination in graphs , 2002, Discret. Math..