Skew throttling

TL;DR

This paper investigates skew zero forcing throttling, characterizing graphs with specific throttling numbers, calculating exact values for certain graph classes, and establishing bounds based on graph diameter.

Contribution

It provides a comprehensive analysis of skew throttling, including characterizations, exact computations for specific graphs, and bounds related to graph diameter.

Findings

Characterized graphs with skew throttling numbers 1, 2, n-1, n

Determined exact skew throttling numbers for paths, cycles, and balanced spiders

Established a sharp lower bound on skew throttling based on diameter

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 sharp lower bound on skew throttling numbers in terms of the diameter.