On comparing variable Zagreb indices for unicyclic graphs (Q2853169)

The first and second Zagreb indices are generalized to the variable Zagreb indices which are defined by \(^{\lambda}M_1(G)=\sum_{u\in V}(d(u))^{2\lambda}\) and \(^{\lambda}M_2(G)=\sum_{u v\in E}(d(u)d(v))^{\lambda}\), where \(\lambda\) is any real number.NEWLINENEWLINE Comparing variable Zagreb indices for unicyclic graphs, it is proved that \(^{\lambda}M_1(G)/n\geq{}^{\lambda}M_2(G)/m\) for \(\lambda\in(-\infty, 0)\), \(^{\lambda}M_1(G)/n\leq{}^{\lambda}M_2(G)/m\) for \(\lambda\in[0, 1]\), and the relationship of the numerical values between \(^{\lambda}M_1(G)/n\) and \(^{\lambda}M_2(G)/m\) is indefinite in the distinct unicyclic graphs when \(\lambda\in(1,+\infty)\).