  A clique covering of a graph $G$ is a set of cliques of $G$ such that any
edge of $G$ is contained in one of these cliques, and the weight of a clique
covering is the sum of the sizes of the cliques in it. The sigma clique cover
number $scc(G)$ of a graph $G$, is defined as the smallest possible weight of a
clique covering of $G$. Let $ K_t(d) $ denote the complete $ t $-partite graph
with each part of size $d$. We prove that for any fixed $d \ge 2$, we have
$$\lim_{t \rightarrow \infty} scc(K_t(d))= \frac{d}{2} t\log t.$$ This
disproves a conjecture of Davoodi, Javadi and Omoomi.
