  We define $PC$-polynomial of graph which is related to clique, (in)dependence
and matching polynomials. The growth rate of partially commutative monoid is
equal to the largest root $\beta(G)$ of $PC$-polynomial of the corresponding
graph.
  The random algebra is defined in such way that its growth rate equals the
largest root of $PC$-polynomial of random graph. We prove that for almost all
graphs all sufficiently large real roots of $PC$-polynomial lie in
neighbourhoods of roots of $PC$-polynomial of random graph. We show how to
calculate the series expansions of the latter roots. The average value of
$\beta(G)$ over all graphs with the same number of vertices is computed.
  We found the graphs on which the maximal value of $\beta(G)$ with fixed
numbers of vertices and edges is reached. From this, we derive the upper bound
of $\beta(G)$. Modulo one assumption, we do the same for minimal value of
$\beta(G)$.
  We study the Nordhaus---Gaddum bounds of $\beta(G)+\beta(\bar{G})$ and
$\beta(G)\beta(\bar{G})$.
