For a connected graph G, the Mostar index Mo(G) and the irregularity irr(G) are defined as \(Mo(G)=\sum _{uv\in E(G)}|n_u-n_v|\) and \( irr (G)=\sum _{uv\in E(G)}|d_u-d_v|\), respectively, where \(d_u\) is the degree of the vertex u of G and \(n_u\) denotes the number of vertices of G which are closer to u than to v for an edge uv. In this paper, we focus on the difference \(\Delta M(G)=Mo(G)- irr (G)\) of graphs G. For trees T of order n, we characterize the minimum and second minimum \(\Delta M(T)\) of T and the minimum \(\Delta M(Tr(T))\) of the triangulation graphs Tr(T). The parity of \(\Delta M\) of cactus graphs is also reported. The effect on \(\Delta M\) is studied for two local operations of subdivision and contraction of an edge in a tree. A formula for \(\Delta M(S(T))\) of the subdivision trees S(T) and the upper and lower bounds on \(\Delta M(S(T))- \Delta M(T)\) are determined with the corresponding extremal trees T. Moreover, three related open problems are proposed to \(\Delta M\) of graphs.

对于连通图G，莫斯塔尔指数Mo（G）和不规则性irr（G）定义为\（Mo（G）= \ sum _ {uv \ in E（G）} | n_u-n_v | \）和\（IRR（G）= \总和_ {UV \在E（G）} | d_u-d_v | \） ，分别，其中\（d_u \）为顶点的程度ü的ģ和\（n_u \）表示对于边uv，G的顶点数量，这些顶点与u相比更接近于v。在本文中，我们关注图G的差异\（\ Delta M（G）= Mo（G）-irr（G）\）。树木Ť的顺序Ñ，我们描述的最小值和第二最小\（\德尔塔M（T）\）的Ť和最小\（\德尔塔M（TR（T））\）三角测量的曲线图Tr的（Ť） 。还报告了仙人掌图的\（\ Delta M \）的奇偶性。对于树中边缘的细分和收缩的两个局部操作，研究了对\（\ Delta M \）的影响。细分树S（T）\（\ Delta M（S（T））\）的公式以及\（\ Delta M（S（T））-\ Delta M（T）\ ）用相应的极值树T确定。此外，对图的\（\ Delta M \）提出了三个相关的开放问题。