$G$ will be denoted by $t(G)$, $b(G)$, $a(G)$, and $l(G)$, respectively. Moreover, a catacondensed benzenoid graph or a phenylene is called a *linear chain* if it does not contain angular or branched hexagons. A *segment* in a catacondensed benzenoid graph or a phenylene $G$ is any maximal linear chain which is a subgraph of $G$. Finally, the number of all the segments of $G$ will be denoted by $s(G)$. Obviously, for the graph from Figure \[benzenoid\] it holds $t(G)=3$, $b(G)=a(G)=l(G)=1$, $s(G)= 4$ and the same is true for the graph from Figure \[phenylene\].

For any $k \geq 0$, the number of vertices of a graph $G$ which have degree $k$ will be denoted by $n_k(G)$. We can now state the following proposition.

[@gut] \[gut-ben\] If $G$ is a benzenoid graph, then $|V(G)|  =  4h(G) + 2 - n_i(G)$, $ |E(G)|  =  5h(G) + 1 - n_i(G)$, $n_3(G)  =  2h(G) - 2$, and $n_2(G)  =  2h(G) + 4 - n_i(G)$.

In [@gut] Proposition \[gut-ben\] was proved just for benzenoid graphs that can be embedded into the regular hexagonal lattice. However, the same proof works for any benzenoid graph.

Using Proposition \[gut-ben\] it is possible to derive similar formulas also for phenylenes.

