  For a graph $X$ without isolated vertices and without isolated edges, a
product-irregular labelling $\omega:E(X)\rightarrow \{1,2,\ldots,s\}$, first
defined by Anholcer in 2009, is a labelling of the edges of $X$ such that for
any two distinct vertices $u$ and $v$ of $X$ the product of labels of the edges
incident with $u$ is different from the product of labels of the edges incident
with $v$. The minimal $s$ for which there exist a product irregular labeling is
called the product irregularity strength of $X$ and is denoted by $ps(X)$.
Clique cover number of a graph is the minimum number of cliques that partition
its vertex-set. In this paper we prove that connected graphs with clique cover
number $2$ or $3$ have the product-irregularity strength equal to $3$, with
some small exceptions.
