The structure and parameters of a graph assigned to topological spaces
نویسندگان
1 Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34148 - 96818, I. R. Iran
2 Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34148 - 96818, I. R. Iran
3 Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin, 34148 - 96818, I. R. Iran
doi
10.22061/jdma.2025.11791.1116چکیده
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 $T_1$.
