  Let G be a simple connected molecular graph with vertex set $V(G)$ and edge
set $E(G)$. One important modification of classical Zagreb index, called hyper
Zagreb index $HM(G)$ is defined as the sum of squares of the degree sum of the
adjacent vertices, that is, sum of the terms $[{d_G}(u)+{d_G}(v)]^2$ over all
the edges of $G$, where ${d_G}(u)$ denote the degree of the vertex $u$ of $G$.
In this paper, the hyper Zagreb index of certain bridge and chain graphs are
computed and hence using the derived results we compute the hyper Zagreb index
of several classes of chemical graphs and nanostructures.
