Gamma-set Domination Graphs I: Complete Biorientations of $q$-Extended Stars and Wounded Spider Graphs

Abstract

The domination number of a graph $G$, $\gamma (G)$, and the domination graph of a digraph $D$, $dom(D)$, are integrated in this paper. The $\gamma$-set di domination graph of the complete biorientation of a graph $G$, $do{m}_{\gamma }(\overleftrightarrow{G})$, is created. All $\gamma$-sets of specific trees $T$ are found, and $do{m}_{\gamma }(\overleftrightarrow{T})$ is characterized for those classes.