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The zero
forcing numbers and propagation times of gear graphs and helm
graphs
Sara Anderton, Rilee Burden, McKenzie Fontenot, Noah Fredrickson, Alexandria Kwon, Sydney Le, Kanno Mizozoe, Erin Raign, August Sangalli, Houston Schuerger and Andrew Schwartz |
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Vol. 19 (2026), No. 2, 275–296
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Abstract |
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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 determine the zero forcing numbers and propagation times of two infinite classes of graphs called gear graphs and helm graphs. |
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Keywords
graph classes, zero forcing, propagation time, relaxed
chronology, chain set
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Mathematical Subject Classification
Primary: 05C50, 05C57, 05C69
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Milestones
Received: 14 April 2024
Revised: 9 September 2024
Accepted: 17 September 2024
Published: 8 March 2026
Communicated by Ann N. Trenk
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Authors |
| Sara Anderton | |
| Department of Mathematics Southeast Missouri State University Cape Girardeau, MO United States |
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| Rilee Burden | |
| Department of Mathematics University of North Texas Denton, TX United States |
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| McKenzie Fontenot | |
| Department of Mathematics University of North Texas Denton, TX United States |
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| Noah Fredrickson | |
| Flower Mound, TX United States |
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| Alexandria Kwon | |
| Little Elm, TX United States |
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| Sydney Le | |
| Department of Electrical and
Computer Engineering Rice University Flower Mound, TX United States |
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| Kanno Mizozoe | |
| Department of Mathematics Trinity College Hartford, CT United States |
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| Erin Raign | |
| Department of Mathematics University of North Texas Denton, TX United States |
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| August Sangalli | |
| Department of Mathematics University of Denver Denver, CO United States |
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| Houston Schuerger | |
| Department of Mathematics Tarleton State University Stephenville, TX United States |
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| Andrew Schwartz | |
| Department of Mathematics Southeast Missouri State University Cape Girardeau, MO United States |
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| © 2026 MSP (Mathematical Sciences Publishers). |
