Restricted 2-fault diameter of hypercubes

This research is supported by the National College Students' Innovation and Entrepreneurship Training Program (S202410530093), the National Natural Science Foundation of China(12301453), the Project of Education Department of Hunan Province(22B0180, 23B0125), the Project of Hunan Provincial Natural Science Foundation of China (2021JJ40522), the Project of Scientific Research Fund of Hunan Provincial Science and Technology Department (No. 2018WK4006), the 111 Project (No. D23017). The fault diameter is a measure in graph theory and network design that evaluates the robustness of a network's diameter. It addresses how the network's efficiency degrades under worst-case failure scenarios, ensuring critical systems maintain performance despite faults. In this paper, we consider the restricted fault diameter of the n-dimensional hypercube network Qn(n≥4). We show that the diameter Qn−F is no more than n + 3 for any F⊆V(Qn) with δ(Qn−F)≥2 and |F|≤4n−9.