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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2508.21764 |
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| _version_ | 1866911590104694784 |
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| author | Moon, Eric J. Bhoumik, Soumya Flesher, Paul |
| author_facet | Moon, Eric J. Bhoumik, Soumya Flesher, Paul |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreversible $k$-Threshold Dynamics on Corona and Base-$b$ Corona Product Graphs Moon, Eric J. Bhoumik, Soumya Flesher, Paul Combinatorics 68R10, 05C70, 05C69, 05C90 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. |
| title | Irreversible $k$-Threshold Dynamics on Corona and Base-$b$ Corona Product Graphs |
| topic | Combinatorics 68R10, 05C70, 05C69, 05C90 |
| url | https://arxiv.org/abs/2508.21764 |