The zero forcing numbers and propagation times of gear graphs and helm graphs
arxiv(2023)
摘要
Zero forcing is a dynamic coloring process on graphs. Initially, each vertex
of a graph is assigned a color of either blue or white, and then a process
begins by which blue vertices force white vertices to become blue. The zero
forcing number is the cardinality of the smallest set of initially blue
vertices which can force the entire graph to become blue, and the propagation
time is the minimum number of steps in such a zero forcing process. In this
paper we will determine the zero forcing numbers and propagation times of two
infinite classes of graphs called gear graphs and helm graphs.
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