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<p>Recently, a bipartite walk on a bipartite graph <i>G</i> was introduced, and the periodicity of its time evolution matrix was discussed. We present a formula for the time evolution matrix of the bipartite walk on a bipartite graph, and so give its spectra. As an application, we present a formula for the time evolution matrix of the bipartite walk on a semiregular bipartite graph, and so give its spectra. Furthermore, we study a relation between the Grover walk and the bipartite walk on a bipartite graph. Finally, we present a formula for the time evolution matrix of the bipartite walk on a regular covering of a bipartite graph.</p>

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The spectra of the time evolution matrix of a bipartite walk on a bipartite graph

  • 期刊论文

  • 发表日期：

    2026年7月31日

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  • Takako Endo,
  • Takashi Komatsu,
  • Norio Konno,
  • Iwao Sato

摘要

Recently, a bipartite walk on a bipartite graph G was introduced, and the periodicity of its time evolution matrix was discussed. We present a formula for the time evolution matrix of the bipartite walk on a bipartite graph, and so give its spectra. As an application, we present a formula for the time evolution matrix of the bipartite walk on a semiregular bipartite graph, and so give its spectra. Furthermore, we study a relation between the Grover walk and the bipartite walk on a bipartite graph. Finally, we present a formula for the time evolution matrix of the bipartite walk on a regular covering of a bipartite graph.