Extremal quasi-unicyclic graphs with respect to the general multiplicative Zagreb indices (Q2104938)

The general multiplicative Zagreb indices are modified versions of the famous Zagreb indices, which are defined as \[ P^\alpha_1(G)=\prod_{u\in V(G)}d_G(u)^\alpha\] and \[P^\alpha_2(G)=\prod_{uv\in E(G)}(d_G(u)d_G(v))^\alpha, \] where they are respectively called the first and second general multiplicative Zagreb indices. In this paper, the authors study the minimum and maximum values of these two indices for quasi-unicyclic graphs with a given order, a fixed number of pendant vertices, and perfect matchings. As a result, they give the corresponding extremal quasi-unicyclic graphs.