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<p>We consider the zeta function associated with the time evolution matrix of a bipartite walk on a bipartite graph and derive a formula for its absolute zeta function. Furthermore, we give formulas for the absolute zeta functions of the zeta functions of the time evolution matrices of bipartite walks on the complete bipartite graph and an even cycle graph. As an application, we obtain formulas for the absolute zeta functions of the zeta functions of the Grover matrices of the complete bipartite graph and an even cycle graph.</p>

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The absolute zeta function with respect to a bipartite walk on a bipartite graph

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月4日

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  • Jiro Akahori,
  • Norio Konno,
  • Iwao Sato,
  • Yuma Tamura,
  • Xinmiao Zhang

摘要

We consider the zeta function associated with the time evolution matrix of a bipartite walk on a bipartite graph and derive a formula for its absolute zeta function. Furthermore, we give formulas for the absolute zeta functions of the zeta functions of the time evolution matrices of bipartite walks on the complete bipartite graph and an even cycle graph. As an application, we obtain formulas for the absolute zeta functions of the zeta functions of the Grover matrices of the complete bipartite graph and an even cycle graph.