标题： 基于边-顶点度的Zagreb指数和图运算 显示英文标题

标题： Edge-vertex degree based Zagreb index and graph operations

摘要： 一个图 $G$ 由两部分组成，顶点和边。 顶点构成顶点集 $V(G)$，边构成边集。 一条边 \( e=xy \)， \( ev \)-支配不仅与其相关的顶点，而且还支配与 \( x \)或 \( y \)相邻的顶点。 边-顶点度的$e,$ $deg^{ev}_{G}(e),$是$ev$支配集中的顶点数$e$。 本文中，我们计算了若干一元和二元图运算的$ev$度版本的 Zagreb 指数的表达式。 显示英文摘要

摘要： A graph $G$ consists of two parts, the vertices and edges. The vertices constitute the vertex set $V(G)$ and the edges, the edge set. An edge \( e=xy \), \( ev \)-dominates not only the vertices incident to it but also those adjacent to either \( x \) or \( y \). The edge-vertex degree of $e,$ $deg^{ev}_{G}(e),$ is the number of vertices in the $ev$-dominating set of $e$. In this article, we compute expressions for the $ev$-degree version of the Zagreb index of several unary and binary graph operations.