  Two inequalities bridging the three isolated graph invariants, incidence
chromatic number, star arboricity and domination number, were established.
Consequently, we deduced an upper bound and a lower bound of the incidence
chromatic number for all graphs. Using these bounds, we further reduced the
upper bound of the incidence chromatic number of planar graphs and showed that
cubic graphs with orders not divisible by four are not 4-incidence colorable.
The incidence chromatic numbers of Cartesian product, join and union of graphs
were also determined.
