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arXiv · 1211.4618

Zero forcing for inertia sets

Steve Butler·Jason Grout·H. Tracy Hall
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Abstract

Zero forcing is a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few "unforced" moves as possible. This leads to a parameter known as the zero forcing number which can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. We introduce a new variation on the zero forcing game which can be used to give an upper bound for the maximum nullity of a matrix associated with a graph that has $q$ negative eigenvalues. This gives some limits to the number of positive eigenvalues that such a graph can have and so can be used to form lower bounds for the inertia set of a graph.

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Steve Butler, Jason Grout, H. Tracy Hall. 2012-11-19. Zero forcing for inertia sets. https://arxiv.org/abs/1211.4618

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