  The $\alpha$-Hermitian adjacency matrix $H_\alpha$ of a mixed graph $X$ has
been recently introduced. It is a generalization of the adjacency matrix of
unoriented graphs. In this paper, we consider a special case of the complex
number $\alpha$. This enables us to define an incidence matrix of mixed graphs.
Consequently, we define a generalization of line graphs as well as a
generalization of the signless Laplacian adjacency matrix of graphs. We then
study the spectral properties of the signless Laplacian adjacency matrix of a
mixed graph. Lastly, we characterize when the signless Laplacian adjacency
matrix of a mixed graph is singular and give lower and upper bounds of number
of arcs and digons in terms of largest and lowest eigenvalue of the signless
Laplacian adjacency matrix.
