Abstract
This poster studies the irreversible k-threshold process on corona-type graph products, where a vertex becomes colored once at least k of its neighbors are colored and then remains colored permanently. We focus on corona, double corona, and base-b corona product graphs built from cycles and complete graphs, with particular attention to how graph structure affects complete activation from a minimum seed set.
A generalized reduction lemma is used to relate threshold dynamics on layered corona graphs to smaller residual graphs, yielding explicit formulas for the irreversible k-threshold conversion number on both corona and double corona families. The poster also introduces a probabilistic refinement, Pk[G], which measures how sensitive complete activation is to the placement of an optimal seed set. This makes it possible to compare graph families not only by the minimum number of seeds required, but also by how reliably optimal seed sets succeed. In particular, even when matched corona and double corona graphs have the same order and size, their probabilistic behavior can differ substantially.
Faculty Advisor
Dr. Soumya Bhoumik, Dr. Paul Flesher
Department/Program
Math
Submission Type
in-person poster
Date
4-10-2026
Rights
Copyright the Author(s)
Recommended Citation
Moon, Eric J.; Bhoumik, Soumya; and Flesher, Paul
(2026)
"Irreversible k-Threshold Dynamics on Corona and Base-b Corona Product Graphs,"
SACAD: Scholarly Activities: Vol. 2026, Article 51.
Available at:
https://scholars.fhsu.edu/sacad/vol2026/iss2026/51
Included in
Discrete Mathematics and Combinatorics Commons, Dynamic Systems Commons, Probability Commons
