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arXiv · 1906.11083

Using Markov chains to determine expected propagation time for probabilistic zero forcing

Yu Chan·Emelie Curl·Jesse Geneson·Leslie Hogben·Kevin Liu·Issac Odegard·Michael S. Ross
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Abstract

Zero forcing is a coloring game played on a graph where each vertex is initially colored blue or white and the goal is to color all the vertices blue by repeated use of a (deterministic) color change rule starting with as few blue vertices as possible. Probabilistic zero forcing yields a discrete dynamical system governed by a Markov chain. Since in a connected graph any one vertex can eventually color the entire graph blue using probabilistic zero forcing, the expected time to do this studied. Given a Markov transition matrix for a probabilistic zero forcing process, we establish an exact formula for expected propagation time. We apply Markov chains to determine bounds on expected propagation time for various families of graphs.

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Yu Chan, Emelie Curl, Jesse Geneson, Leslie Hogben, Kevin Liu, Issac Odegard, Michael S. Ross. 2019-06-25. Using Markov chains to determine expected propagation time for probabilistic zero forcing. https://arxiv.org/abs/1906.11083

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