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This study investigates unicyclic graphs with Szeged complexity 2, providing a structured classification of bipartite unicyclic graphs and categorizing the non-bipartite cases with cycles of lengths 3 and 5. Furthermore, we establish the bounds for the Wiener complexity of bipartite unicyclic graphs possessing the Szeged complexity 2. By refining complexity rankings and analyzing structural differences, this research offers valuable insights for graph-based models in various scientific disciplines.
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Vaziri et al. (2026) studied this question.
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