The zero forcing numbers and propagation times of gear graphs and helm graphs

Involve a Journal of Mathematics 2026 Open access

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Authors: Sara Anderton, Rilee Burden, McKenzie Fontenot, Noah Fredrickson, Alexandria Kwon, Sydney Le, Kanno Mizozoe, Erin Raign, August Sangalli, Houston Schuerger, Andrew Schwartz
DOI: 10.2140/involve.2026.19.275
Cited by: 0
References: 7

Abstract

Zero forcing is a dynamic coloring process on graphs. Initially, each vertex of a graph is assigned a color of either blue or white, and then a process begins by which blue vertices force white vertices to become blue. The zero forcing number is the cardinality of the smallest set of initially blue vertices which can force the entire graph to become blue, and the propagation time is the minimum number of steps in such a zero forcing process. In this paper we will determine the zero forcing numbers and propagation times of two infinite classes of graphs called gear graphs and helm graphs.

Fields of Study & Subjects

Advanced Graph Theory Research Graph Labeling and Dimension Problems

Publication details

Journal / source
Involve a Journal of Mathematics
Volume
19
Issue
2
Pages
275–296
Publication date
8 March 2026
Language
EN