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July 6, 2026European Journal of MathematicsOpen Access

Isometric embeddings of resonance graphs as finite distributive lattices

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Authors

ZCZhongyuan Che

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Overview

Randomized trial shows isometric dimension of resonance graphs in bipartite graphs, indicating embedding measures.

Key Points

  • This research aims to explore the isometric embedding characteristics of resonance graphs derived from plane bipartite graphs.
  • Analyzed the relationship between resonance graphs and finite distributive lattices.
  • Determined the isometric dimension of connected resonance graphs, establishing bounds based on face counts.
  • Developed an algorithm for binary coding on vertex sets to achieve the isometric embedding into hypercubes.
  • Connected resonance graph R(G) exhibits isometric dimension at least n0(G).
  • The lower bound is reached when G is a weakly elementary bipartite graph with specific infinite face properties.
  • An algorithm successfully enables embedding R(G) into hypercubes of dimension n0(G).

Cite This Study

Zhongyuan Che (2026) studied this question.

synapsesocial.com/papers/6a4b44fa997070ff83b5ae84https://doi.org/10.1007/s40879-026-00911-7
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