讲座内容：

We present Lambda-positive noncommutative analogs of the chromatic symmetric function of some graphs, which implies both the $e$-positivity and Schur positivity of the graphs. It often turns out that certain noncommutative analog has a concise formula, which implies a convenient way of calculating explicit $e$-coefficients and a new approach of confirming the $e$-positivity of graphs of special structures.