The concept of domination in graphs plays a central role in understanding structural properties and applications in network theory. In this study, we focus on the paired disjunctive domination number in the context of middle graphs, a transformation that captures both adjacency and incidence relations of the original graph. We begin by investigating this parameter for middle graphs of several special graph classes, including path graphs, cycle graphs, wheel graphs, complete graphs, complete bipartite graphs, star graphs, friendship graphs, and double star graphs. We then present general results by establishing lower and upper bounds for the paired disjunctive domination number in middle graphs of arbitrary graphs, with particular emphasis on trees. Additionally, we determine the exact value of the parameter for middle graphs obtained through the join operation. These findings contribute to the broader understanding of domination-type parameters in transformed graph structures and offer new insights into their combinatorial behavior.

翻译：图的支配概念在理解网络理论中的结构性质和应用中占据核心地位。本研究聚焦于中间图的配对析取支配数，中间图作为一种变换，同时捕捉了原图的邻接关系与关联关系。我们首先探究了若干特殊图类中间图的该参数，包括路径图、环图、轮图、完全图、完全二分图、星图、友谊图及双星图。随后，通过建立任意图（尤其是树）中间图的配对析取支配数的上下界，我们给出了普适性结论。此外，我们还确定了通过连接操作得到的中间图该参数的精确值。这些发现深化了对变换图结构中支配型参数的理解，并为其组合行为提供了新的见解。