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14 June 2023 Gröbner bases method for solving N-path in finite graph and its application
Zhiqin Zhao, Xuewei Xiong
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Proceedings Volume 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023); 127250N (2023) https://doi.org/10.1117/12.2679167
Event: International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 2023, Suzhou, China
Abstract
Let G be a finite directed graph with no loop and no heavy edges, or an undirected graph with no loops and no edges. 𝑁 is a given natural number. This paper proves that the existence problem of two paths with length 𝑁 in G (referred to as 𝑁-path) is completely equivalent to the solutions of a multivariate of polynomial 𝑁 the range of {0,1} or {0,1, −1}. Therefore, the Gröbner bases method can be used to give an effective discrimination of the existence of the solution. This result can be applied to solve the problems of cutting edge judgment, tree and forest judgment in G.
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Zhiqin Zhao and Xuewei Xiong "Gröbner bases method for solving N-path in finite graph and its application", Proc. SPIE 12725, International Conference on Pure, Applied, and Computational Mathematics (PACM 2023), 127250N (14 June 2023); https://doi.org/10.1117/12.2679167
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Matrices
Biomedical applications
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Computer programming
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