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Zagreb indices and their modified versions of a molecular graph are important molecular descriptors which can be applied in characterizing the structural properties of organic compounds from different aspects. In this article, by exploring the structures of the quasi-tree graphs with given different parameters (order, perfect matching and number of pendant vertices) and using the properties of the general multiplicative Zagreb indices, we determine the minimal and maximal values of general multiplicative Zagreb indices on quasi-tree graphs with given order, with perfect matchings, and with given number of pendant vertices. Furthermore, we present the minimal and maximal values of general multiplicative Zagreb indices on trees with perfect matchings.

Quasi-Tree Graphs With Extremal General Multiplicative Zagreb Indices