• Corpus ID: 117054281

Iteration Index of a Zero Forcing Set in a Graph

@article{Chilakamarri2011IterationIO,
  title={Iteration Index of a Zero Forcing Set in a Graph},
  author={Kiran B. Chilakamarri and Nathaniel Dean and Cong X. Kang and Eunjeong Yi},
  journal={arXiv: Combinatorics},
  year={2011}
}

• K. Chilakamarri, N. Dean, +1 author Eunjeong Yi
• Published 8 May 2011
• Mathematics
• arXiv: Combinatorics

Let each vertex of a graph G = (V (G),E(G)) be given one of two colors, say, “black” and “white”. Let Z denote the (initial) set of black vertices of G. The color-change rule converts the color of a vertex from white to black if the white vertex is the only white neighbor of a black vertex. The set Z is said to be a zero forcing set of G if all vertices of G will be turned black after finitely many applications of the color-change rule. The zero forcing number of G is the minimum of |Z| over all zero forcing sets Z ⊆ V (G). Zero forcing parameters have been studied and applied to the minimum rank problem for graphs in numerous articles. We define the iteration index of a zero forcing set of a graph G to be the number of (global) applications of the color-change rule required to turn all vertices of G black; this leads to a new graph invariant, the iteration index of G – it is the minimum of iteration indices of all minimum zero forcing sets of G. We present some basic properties of the iteration index and discuss some preliminary results on certain graphs.