On graphs with graphic imbalance sequences

The imbalance of the edge $e=uv$ in a graph $G$ is the value $imb\,_{G}(e)=|d_{G}(u)-d_{G}(v)|$. We prove that the sequence $M_{G}$ of all edge imbalances in $G$ is graphic for several classes of graphs including trees, graphs in which all non-leaf vertices form a clique and the so-called complete extensions of paths, cycles and complete graphs. Also, we formulate two interesting conjectures related to graphicality of $M_{G}$.