  In this paper we define two infinite families of graphs called C-$\delta$
graphs and $\delta$- graph and prove that $\delta$-graphs satisfy $\delta$
conjecture. Also we introduce a family of C-$\delta$ graphs from which we can
identify $\delta$ graphs as their complements. Finally we give a list of
C-$\delta$ graphs and the relationship with their minimum semidefinite rank.
