Vertex Vulnerability in Wrapped Butterfly Network

Vulnerability is a critical factor in evaluating the topology of a network. A comprehensive understanding of these vulnerabilities is vital for enhancing the efficiency of network operations. In essence, an increase in a network’s vulnerability correlates with a decrease in its security. The significance of the wrapped butterfly graph, derived from the family of cayley graphs, is evident in its strong symmetry and regularity, making it a highly efficient network with various attributes. This study not only focuses on a theoretical framework for detecting vulnerabilities, but also offers algorithms that tackle these vulnerabilities, centered on the wrapped butterfly graph as a model for interconnection networks. We conduct simulation experiments to assess the performance of these algorithms, exploring different types of vertex vulnerabilities and analyzing the overall robustness of interconnection networks. Identifying vulnerability parameters has been established as NP–complete across numerous graph categories. In this paper, we identify several vertex vulnerability parameters, including integrity, toughness, scattering number, tenacity, and rupture degree, related to the wrapped butterfly graph in polynomial time.