Let G be a (p, q)-graph. Let f be an injective mapping from V(G) to {1, 2, …, p}. For
each edge xy, assign the label ð
x
y
Þ or ð
y
x
Þ according as x > y or y > x. Call f a parity
combination cordial labeling if |ef(0) − ef(1)| ≤ 1, where ef(0) and ef(1) denote the
number of edges labeled with an even number and an odd number, respectively. In
this paper we make a survey on all graphs of order at most six and find out whether
they satisfy a parity combination cordial labeling or not and get an upper bound for
the number of edges q of any graph to satisfy this condition and describe the parity
combination cordial labeling for two families of graphs.