On Delta Graphs and Delta Conjecture

Abstract

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.