catacondensed benzenoid graph with at least two hexagons. If we add *quadrilaterals* (faces whose boundary is a $4$-cycle) between all pairs of adjacent hexagons of $G$, the obtained graph $G'$ is called a *phenylene*, see Figure \[phenylene\]. We then say that $G$ is the *hexagonal squeeze* of $G'$. Obviously, graph $G$ in Figure \[benzenoid\] is the hexagonal squeeze of phenylene $G'$ from Figure \[phenylene\]. For a phenylene $G'$ the *dualist tree* of $G'$ is defined as the dualist tree of its hexagonal squeeze. Moreover, a *hexagon* of $G'$ is any inner face of $G'$ whose boundary is a $6$-cycle.

![\[phenylene\] A phenylene $G'$.](phenylene.eps)

Let $G$ be a catacondensed benzenoid graph or a phenylene and let $h_0$ be a hexagon of $G$. Hexagon $h_0$ is called *terminal* if it is adjacent to exactly one other inner face of $G$ and it is called *branched* if it is adjacent to exactly three other inner faces of $G$. If $h_0$ is adjacent to exactly two other inner faces, it has two vertices of degree two. Then $h_0$ is called *angular* if these two vertices are adjacent and *linear* it they are not adjacent. The number of terminal, branched, angular, and linear hexagons of 