attains its minimum value if and only if $s(G)=1$ and $b(G)=0$, which is true if and only if $G$ is a linear chain.

To find the graphs that attain the maximum value, we introduce special families of catacondensed benzenoid graphs and phenylenes. These families will be defined by the following extensions.

-   **Extension 1:** *Let $G_0$ be a catacondensed benzenoid graph (or a phenylene) and let $h_0$ be an arbitrary terminal hexagon of $G_0$. We denote by $G$ a graph obtained from $G_0$ by attaching exactly two new hexagons to $h_0$ such that $h_0$ becomes a branched hexagon (and in the case of phenylenes, we also add two quadrilaterals between $h_0$ and the two new hexagons). See Figure \[dodas\_dva\].*

    ![\[dodas\_dva\] A catacondensed benzenoid graph (or a phenylene) $G$ obtained from $G_0$ by Extension 1.](dodas_dva.eps)

-   **Extension 2:** *Let $G_0$ be a catacondensed benzenoid graph (or a phenylene) and let $h_0$ be an arbitrary terminal hexagon of $G_0$. We denote by $G$ a graph obtained from $G_0$ by attaching exactly one new hexagon to $h_0$ such that $h_0$ becomes an angular hexagon (and in the case of phenylenes, we also add a quadrilateral between $h_0$ and the new hexagon). See Figure 