Skew throttling

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Date
2020-01-01
Authors
Curl, Emelie
Geneson, Jesse
Hogben, Leslie
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Abstract

Zero forcing is a process that colors the vertices of a graph blue by starting with some vertices blue and applying a color change rule. Throttling minimizes the sum of the number of initial blue vertices and the time to color the graph. In this paper, we study throttling for skew zero forcing. We characterize the graphs of order n with skew throttling numbers 1, 2, n−1, and n. We find the exact skew throttling numbers of paths, cycles, and balanced spiders with short legs. In addition, we find a lower bound on the skew throttling number in terms of the diameter of the graph for graphs of minimum degree at least two.

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This article is published as Curl, Emelie, Jesse Geneson, and Leslie Hogben. "Skew throttling."The Australasian Journal of Combinatorics 78, no. 1 (2020): 177-190. Posted with permission.

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