Let G be a simple graph and let $={G}$ denotes its complement. We say that G is integral if its spectrum consists entirely of integers. If $overline{aK_{a};{igcup};{eta}K_{b}}$ is integral we show that it belongs to the class of integral graphs $[frac{kt}{ au};{x_0};+;frac{mt}{ au};z};K_{(t+{ell}n)+{ell}m};igcup;[frac{kt}{ au};{y_0};+;frac{(t;+;{ell}n)k;+;{ell}m}{ au};z]n;K_{em)$, where (i) t, k, $ell$, m, $n;in;mathbb{N}$ such that (m, n) = 1, (n,t) = 1 and ($ell,;t$) = 1 ; (ii) $ au;=;((t;+;{ell}n)k;+;{ell}m,;mt)$ such that $ au;$mid$kt$</TEX>; (iii) ($x_0,;y_0$) is a particular solution of the linear Diophantine equation $((t;+;{ell}n)k;+;{ell}m)x;-;(mt)y;=; au;and;(iv);z;{geq};{z_0}$ where $z_{0}$ is the least integer such that $(frac{kt}{ au};{x_0};+;frac{mt}{ au};{z_0});geq;1;and;(frac{kt}{ au};{y_0};+;frac{(t+{ell}n)k+{ell}m}{ au};{z_0});geq;1$.