Throttling positive semidefinite zero forcing propagation time on graphs

TL;DR

This paper investigates the positive semidefinite zero forcing throttling process on graphs, establishing bounds and exact values for specific graph classes, and characterizing graphs with extremal throttling numbers.

Contribution

It provides a tight lower bound on positive semidefinite throttling and determines exact throttling numbers for paths, cycles, and binary trees, advancing understanding of graph propagation.

Findings

Established a tight lower bound on throttling number

Determined throttling numbers for paths, cycles, and binary trees

Characterized graphs with extreme throttling numbers

Abstract

Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size of the initial blue vertex set and the number of the time steps needed to color the graph. We study throttling for positive semidefinite zero forcing. We establish a tight lower bound on the positive semidefinite throttling number as a function of the order, maximum degree, and positive semidefinite zero forcing number of the graph, and determine the positive semidefinite throttling numbers of paths, cycles, and full binary trees. We characterize the graphs that have extreme positive semidefinite throttling numbers.