Let G be a finite simple graph on the vertex set \(V(G) = \{x_{1}, \ldots , x_{n}\}\) and match(G), min-match(G) and ind-match(G) the matching number, minimum matching number and induced matching number of G, respectively. Let \(K[V(G)] = K[x_{1}, \ldots , x_{n}]\) denote the polynomial ring over a field K and \(I(G) \subset K[V(G)]\) the edge ideal of G. The relationship between these graph-theoretic invariants and ring-theoretic invariants of the quotient ring K[V(G)]/I(G) has been studied. In the present paper, we study the relationship between match(G), min-match(G), ind-match(G) and \({\hbox {dim}}K[V(G)]/I(G)\).

令G为顶点集\（V（G）= \ {x_ {1}，\ ldots，x_ {n} \} \）和match（G），min-match（G）和ind -match（ģ）匹配数，最小匹配数和导出匹配数ģ分别。令\（K [V（G）] = K [x_ {1}，\ ldots，x_ {n}] \）表示字段K和\（I（G）\子集K [V（G ）] \）G的边缘理想。商环K [ V（G）] / I（）的这些图论不变量和环论不变量之间的关系G）已被研究。在本文中，我们研究了match（G），min-match（G），ind-match（G）和\（{\ hbox {dim}} K [V（G）] / I（G） \）。