A Graph-Theoretical Framework for Identifying Critical Data Center Using Status Unequal Domination

Abstract

Critical nodes are essential components of a graph network as they drive information flow and significantly influence the system’s ability and vulnerability. This work introduces status unequal domination ([Formula: see text]-domination), a new framework for identifying critical nodes based on status (a distance-based parameter). The concepts of the [Formula: see text]-dominating set and [Formula: see text]-domination number [Formula: see text] are established for several graph families, along with the bounds. To strengthen the theoretical foundation, several supporting notions related to [Formula: see text]-based influence are also developed. An algorithm is proposed for determining the minimum [Formula: see text]-dominating set in any connected graph and a modified version is formulated for the lexicographic product [Formula: see text]. The practical effectiveness of the framework is demonstrated through a data-center resilience model, where the method identifies the most crucial data centers for sustaining operation under disruptions. The proposed framework provides a systematic method for identifying critical nodes through Status Unequal Domination offering valuable insights for resilience assessment in complex networked systems.