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An Algorithm for the Numbers of Homomorphisms from Paths to Rectangular Grid Graphs

Author

Listed:
  • Hatairat Yingtaweesittikul

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Sayan Panma

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Penying Rochanakul

    (Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

Let G and H be graphs. A mapping f from the vertices of G to the vertices of H is known as a h o m o m o r p h i s m from G to H if, for every pair of adjacent vertices x and y in G , the vertices f ( x ) and f ( y ) are adjacent in H . A rectangular grid graph is the Cartesian product of two path graphs. In this paper, we provide a formula to determine the number of homomorphisms from paths to rectangular grid graphs. This formula gives the solution to the problem concerning the number of walks in the rectangular grid graphs.

Suggested Citation

  • Hatairat Yingtaweesittikul & Sayan Panma & Penying Rochanakul, 2023. "An Algorithm for the Numbers of Homomorphisms from Paths to Rectangular Grid Graphs," Mathematics, MDPI, vol. 11(11), pages 1-14, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2587-:d:1164447
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    References listed on IDEAS

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    1. Keshavarz-Kohjerdi, Fatemeh & Bagheri, Alireza, 2023. "Finding Hamiltonian cycles of truncated rectangular grid graphs in linear time," Applied Mathematics and Computation, Elsevier, vol. 436(C).
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