In this note, we first show that the general Zagreb index can be obtained from the M−polynomial of a graph by giving a suitable operator. Next, we obtain M−polynomial of some cactus chains. Furthermore, we derive some degree based topological indices of cactus chains from their M−polynomial.

For a molecular graph [Formula: see text], the [Formula: see text]-index or forgotten topological index is defined as the sum of cubes of degree of all vertices of the graph and the hyper-Zagreb index is equal to the sum of square of sum of degree of all adjacent vertices of the graph. In this paper, we obtain [Formula: see text]-index, hyper-Zagreb index and their coindices of [Formula: see text]-tensor products (four new tensor products based on transformations of a graph) of graphs and their complements.

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