We study the discrete quantum walk that assigns negative identity coins to marked vertices and Grover coins to the unmarked ones. We find combinatorial bases for the eigenspaces of the transtion matrix, and derive a formula for the average vertex mixing matrix. We then explore properties of this matrix when the marked vertices or unmarked vertices are neighborhood-equitable in the vertex-deleted subgraph.

翻译：本文研究一种离散量子行走模型，该模型为标记顶点分配负单位硬币算符，为非标记顶点分配Grover硬币算符。我们给出了转移矩阵特征空间的组合基，并推导出平均顶点混合矩阵的闭式表达式。随后，我们探讨了当标记顶点或非标记顶点在顶点删除子图中满足邻域等可配性时，该矩阵所具有的数学性质。