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arXiv · 2501.03472

Sharp bounds for product and sum throttling numbers

Ryan Blair·Gabriel Elvin·Veronika Furst·Leslie Hogben·Nandita Sahajpal·Tony W. H. Wong
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Abstract

Throttling in graphs optimizes a sum or product of resources used, such as the number of vertices in an initial set, and time required, such as the propagation time, to complete a given task. We introduce a new technique to establish sharp upper bounds in terms of graph order for sum throttling and initial cost product throttling for power domination. Furthermore, we establish sharp bounds on possible changes of the product throttling number, both with and without initial cost, caused by certain graph operations for standard zero forcing, positive semidefinite forcing, and power domination.

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Ryan Blair, Gabriel Elvin, Veronika Furst, Leslie Hogben, Nandita Sahajpal, Tony W. H. Wong. 2025-01-14. Sharp bounds for product and sum throttling numbers. https://arxiv.org/abs/2501.03472

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