On the characterization of tricyclic graphs with Szeged complexity one

Document Type : Full Length Article

Author

Department of Mathematics, Factually of Science, Shahid Rajaee Teacher Training University, Tehran, I. R. Iran

Abstract

This paper presents a classification of 12 out of 15 known families of tricyclic graphs based on their Szeged complexity. It is shown that only two of these families contain graphs with Szeged complexity equal to one. Building on previous structural analyses of unicyclic and bicyclic graphs, this study extends the classification framework to include a substantial portion of tricyclic configurations. The results contribute to a deeper understanding of graph complexity and lay the groundwork for further exploration of cyclic graph structures.

Graphical Abstract

On the characterization of tricyclic graphs with Szeged complexity one

Keywords

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Volume 10, Issue 4
December 2025
Pages 393-401
  • Receive Date: 13 September 2025
  • Revise Date: 10 October 2025
  • Accept Date: 23 November 2025
  • First Publish Date: 25 November 2025
  • Publish Date: 01 December 2025