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 $T_1$.
Behtoei, A. , Zarifian, R. and Azami, S. (2025). The structure and parameters of a graph assigned to topological spaces. Journal of Discrete Mathematics and Its Applications, 10(2), 183-194. doi: 10.22061/jdma.2025.11791.1116
MLA
Behtoei, A. , , Zarifian, R. , and Azami, S. . "The structure and parameters of a graph assigned to topological spaces", Journal of Discrete Mathematics and Its Applications, 10, 2, 2025, 183-194. doi: 10.22061/jdma.2025.11791.1116
HARVARD
Behtoei, A., Zarifian, R., Azami, S. (2025). 'The structure and parameters of a graph assigned to topological spaces', Journal of Discrete Mathematics and Its Applications, 10(2), pp. 183-194. doi: 10.22061/jdma.2025.11791.1116
CHICAGO
A. Behtoei , R. Zarifian and S. Azami, "The structure and parameters of a graph assigned to topological spaces," Journal of Discrete Mathematics and Its Applications, 10 2 (2025): 183-194, doi: 10.22061/jdma.2025.11791.1116
VANCOUVER
Behtoei, A., Zarifian, R., Azami, S. The structure and parameters of a graph assigned to topological spaces. Journal of Discrete Mathematics and Its Applications, 2025; 10(2): 183-194. doi: 10.22061/jdma.2025.11791.1116
)
)