On Integral Graphs which Belong to the Class $\overline {\alpha K_{a,a,a}\cup \beta K_{b,b,b}}$

Abstract:

      Let $G$ be a simple graph and let $\overline G$ denote its complement. We say that $G$ is integral if its spectrum consists entirely of integers. In this work we establish a characterization of integral graphs which belong to the class $\overline {\alpha K_{a,a,a} \cup\beta K_{b,b,b}}$, where $mG$ denotes the $m$-fold union of the graph $G$.