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Let G be a simple connected molecular graph with vertex set $V(G)$ and edgeset $E(G)$. One important modification of classical Zagreb index, called hyperZagreb index $HM(G)$ is defined as the sum of squares of the degree sum of theadjacent vertices, that is, sum of the terms $[{d_G}(u)+{d_G}(v)]^2$ over allthe 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 arecomputed and hence using the derived results we compute the hyper Zagreb indexof several classes of chemical graphs and nanostructures.

Hyper Zagreb Index of Bridge and Chain Grpahs