The structures of many molecules such as dendrimers, alkanes and acyclic molecules are like trees. Rooted trees have wide applications in chemical graph theory such as enumeration and encoding of chemical structures. Structures of chemical compounds can be systematized in form of chemical and empirical formulae through mathematical means. Chemists have a long tradition of using atomic valences (vertex degrees) to find molecular structures graphically.
In structural chemistry number of graph applications exist. This paper reflects the work on the following indices: first general Zagreb index Mα, general Randić connectivity index Rα, general sum-connectivity index χα, atom-bond connectivity index ABC, geometric-arithmetic index GA, fourth atom-bond connectivity index ABC4, fifth geometric-arithmetic index GA5, hyper-Zagreb index HM (G), first multiple Zagreb index PM1 (G), second multiple Zagreb index PM2 (G) and Zagreb polynomials M1 (G, x) , M1 (G, x) for line graph of complete m-ary tree.
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