The first general multiplicative Zagreb index of a graph G is defined as \(P_1^a (G) = \prod _{v \in V(G)} (deg_G (v))^a\) and the second general multiplicative Zagreb index is \(P_2^a (G) = \prod _{v \in V(G)} (deg_G (v))^{a \, deg_G (v)}\), where V(G) is the vertex set of G, \(deg_{G} (v)\) is the degree of v in G and \(a \ne 0\) is a real number. We present lower and upper bounds on the general multiplicative Zagreb indices for trees and unicyclic graphs of given order with a perfect matching. We also obtain lower and upper bounds for trees and unicyclic graphs of given order and matching number. All the trees and unicyclic graphs which achieve the bounds are presented, thus our bounds are sharp. Bounds for the classical multiplicative Zagreb indices are special cases of our theorems and those bounds are new results as well.

图G的第一个通用乘法Zagreb索引定义为\（P_1 ^ a（G）= \ prod _ {v \ in V（G）}（deg_G（v））^ a \）和第二个通用乘法Zagreb索引是\（P_2 ^ a（G）= \ prod _ {v \ in V（G）}（deg_G（v））^ {a \，deg_G（v）} \），其中V（G）是顶点G的集合，\（deg_ {G}（v）\）是v在G和\（a \ ne 0 \）中的度数是一个实数。我们给出了树木和给定阶数的单环图具有完美匹配的一般乘法Zagreb指数的上下限。我们还获得给定顺序和匹配数的树和单环图的上下界。给出了达到边界的所有树和单环图，因此我们的边界很清晰。经典乘法Zagreb指数的界线是我们定理的特例，这些界线也是新的结果。