%0 Journal Article %T The Noncommuting Graph of Bounded Linear Operators on a Hilbert Space %J Journal of Advanced Mathematical Modeling %I Shahid Chamran University of Ahvaz %Z 2251-8088 %A Raja, Pandora %D 2022 %\ 06/22/2022 %V 12 %N 2 %P 168-174 %! The Noncommuting Graph of Bounded Linear Operators on a Hilbert Space %K Noncommuting graph %K Hilbert space %K Operators %K Compact Operators %K Fredholm Operators %R 10.22055/jamm.2022.39417.1987 %X Let $EuScript{H}$ be a Complex Hilbert space and $EuScript{B(H)}$ be the algebra of allbounded linear operators on $EuScript{H}$. The non-commuting graph of $EuScript{B(H)}$, denoted by $mathnormal{Gamma}(EuScript{B(H)})$ is a graph whose vertices are non-scalar bounded operators and two distinct vertices $A$ and $B$ are adjacent if and only if $AB neq BA$. In this paper, we prove the connectivity of $mathnormal{Gamma}(EuScript{B(H)})$ for separable and non-separable complex Hilbert spaces. Also we show that the noncommuting graphs of the set of all finite rank operators on $EuScript{H}$, the set of all compact operators on $EuScript{H}$, the set of all non-invertible operators on $EuScript{H}$ and the set of all Fredholm operators on $EuScript{H}$ are connected graphs. %U https://jamm.scu.ac.ir/article_17543_33aaeebb0a646846a1ddefb76402f9c5.pdf