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arXiv · 2508.21764

Irreversible $k$-Threshold Dynamics on Corona and Base-$b$ Corona Product Graphs

Eric J. Moon·Soumya Bhoumik·Paul Flesher
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Abstract

We study the irreversible $k$-threshold process on corona-type graph products, including the corona product, the double corona product, and a generalized base-$b$ corona construction. Exact results are obtained for the irreversible $k$-threshold conversion number on corona and double corona product graphs through reduction lemmas that relate these graphs to smaller corona-type instances and to classical base graphs. The base-$b$ construction provides a unified framework extending the corona and double corona cases. A probabilistic refinement is also considered by studying the likelihood that a uniformly chosen minimum seed set yields complete activation. These results show how layered attachment structure influences both deterministic conversion behavior and probabilistic saturation in corona-type graph products.

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Eric J. Moon, Soumya Bhoumik, Paul Flesher. 2025-08-29. Irreversible $k$-Threshold Dynamics on Corona and Base-$b$ Corona Product Graphs. https://arxiv.org/abs/2508.21764

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