### Four new operations related to composition and their reformulated Zagreb index

#### Abstract

The first reformulated Zagreb index *E**M*_{1}(*G*) of a simple graph *G* is defined as the sum of the terms (*d*_{u} + *d*_{v} − 2)^{2} over all edges *u**v* of *G*. In 2017, Sarala et al. introduced four new operations(*F*-product) of graphs. In this paper, we study the first reformulated Zagreb index for the *F*-product of some special well-known graphs such as subdivision and total graph.

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DOI: http://dx.doi.org/10.19184/ijc.2018.2.1.5

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