论文信息 - A technique for computing the zero forcing number of a graph with a cut-vertex

A technique for computing the zero forcing number of a graph with a cut-vertex

Abstract The zero forcing number of a graph is the minimum size of a zero forcing set. This parameter is useful in the minimum rank/maximum nullity problem, as it gives an upper bound to the maximum nullity. Results for determining graphs with extreme zero forcing numbers, for determining the zero forcing number of graphs with a cut-vertex, and for determining the zero forcing number of unicyclic graphs are presented.

Darren D. Row

[1] Shaun M. Fallat,et al. On the difference between the maximum multiplicity and path cover number for tree-like graphs , 2005 .

[2] Leslie Hogben,et al. Vertex and edge spread of zero forcing number, maximum nullity, and minimum rank of a graph , 2012 .

[3] Vittorio Giovannetti,et al. Full control by locally induced relaxation. , 2007, Physical review letters.

[4] Hong-Gwa Yeh,et al. On minimum rank and zero forcing sets of a graph , 2010 .

[5] Shaun M. Fallat,et al. Zero forcing parameters and minimum rank problems , 2010, 1003.2028.

[6] Shaun M. Fallat,et al. The minimum rank of symmetric matrices described by a graph: A survey☆ , 2007 .

[7] Koji Maruyama,et al. Indirect Hamiltonian identification through a small gateway , 2009, 0903.0612.

[8] Charles R. Johnson,et al. The graphs for which the maximum multiplicity of an eigenvalue is two , 2007, math/0701562.

[9] Shaun M. Fallat,et al. On the minimum rank of not necessarily symmetric matrices : a preliminary study , 2009 .

[10] L. Hogben. Minimum Rank Problems , 2010 .

[11] Simone Severini,et al. Nondiscriminatory propagation on trees , 2008, 0805.0181.