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arXiv · 1705.10391

Zero forcing number of graphs

Thomas Kalinowski·Nina Kamčev·Benny Sudakov
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Abstract

A subset $S$ of initially infected vertices of a graph $G$ is called forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbour, infects this neighbour. The forcing number of $G$ is the minimum cardinality of a forcing set in $G$. In the present paper, we study the forcing number of various classes of graphs, including graphs of large girth, $H$-free graphs for a fixed bipartite graph $H$, random and pseudorandom graphs.

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Thomas Kalinowski, Nina Kamčev, Benny Sudakov. 2017-06-05. Zero forcing number of graphs. https://arxiv.org/abs/1705.10391

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