Fault tolerance diagnosis plays a crucial role in maintaining the safe operation of interconnection networks. In 2024, Zheng et al. introduced the concept of non-inclusive \(g\) -extra diagnosability, a novel measure for assessing network reliability, and provided a solution for determining the non-inclusive \(g\) -extra diagnosability of network graphs under the PMC model. However, this method is applicable to fewer types of networks. In this paper, we present a general method for determining the non-inclusive 1-extra diagnosability of regular networks. This method has broad applications and is suitable for various well-known networks, such as data center networks, \(k\) -ary \(n\) -cube, hypercube-like networks, DQcube, dual-cube, and others.
