有关欧拉图Q-道矩阵Smith标准型的性质研究
Properties of the Smith Normal Form of the Q-Walk Matrix in Euler Graphs
摘要: 对n阶欧拉图G，考虑其对应的Q-道矩阵，这里Q为图G的无符号拉普拉斯矩阵，e为n维全一列向量。本文给出当WQ的行列式满足，其中b为奇数且不含平方因子时，WQ的Smith标准型为。
Abstract: Let G be an Euler Graph with n vertices. The Q-walk matrix WQ of G is the matrix , where Q is the Signless Laplacian matrix of G and e is the all-one vector. We show that determinant of WQ satisfies , where b is odd and square-free, then the Smith normal form of WQ is .
文章引用：魏靖园, 吕思澄. 有关欧拉图Q-道矩阵Smith标准型的性质研究[J]. 理论数学, 2024, 14(3): 252-259. https://doi.org/10.12677/pm.2024.143103

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