The structure and parameters of a graph assigned to topological spaces

Document Type : Full Length Article

Authors

Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34148 - 96818, I. R. Iran

Abstract

For a set ‎$‎X‎$ ‎and a ‎topological space ‎$‎(X,\tau‎)$, ‎let‎ ‎‎$‎\Gamma_{_X}(\tau)‎$ ‎be a‎ ‎graph ‎with ‎vertex ‎set ‎‎$‎\tau\setminus \{\emptyset,X\}‎$ ‎in ‎which ‎two ‎vertices ‎‎$‎A_1‎$ ‎and ‎‎$‎A_2‎$ ‎are ‎adjacent ‎just ‎when ‎‎$‎A_1\cup A_2=X‎$‎. In this paper and among some other results, we study the maximum and minimum degrees, the matching number, the chromatic number, the chromatic index, ‎the planarity, the Wiener index and the Zagreb index of ‎‎$‎\Gamma_{_X}(\tau)‎$ and we determine their exact values in general cases or in some special topological spaces like ‎$‎T_1‎$‎‎.

Graphical Abstract

The structure and parameters of a graph assigned to topological spaces

Keywords

Main Subjects


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Volume 10, Issue 2
June 2025
Pages 183-194
  • Receive Date: 25 February 2025
  • Revise Date: 22 April 2025
  • Accept Date: 30 April 2025
  • First Publish Date: 01 June 2025
  • Publish Date: 01 June 2025