New families of adjointly unique graphs Original Research Article

Let Dn be the graph obtained from the union of Pn−2 and K3 by identifying a vertex of K3 with an endvertex of Pn−2. We show that the graph (⋃ri=1Pli) ∪ (⋃sj=1 Cmj ∪ (⋃tk=1Dnk) is adjointly unique under certain conditions, thereby establishing the chromatic uniqueness of its complement.