The Tenacity of Generalized Petersen Graphs

Communication networks can be represented as graphs, where vertices representnetwork nodes and edges represent connections between them. Various graphtheory parameters, such as connectivity, toughness, tenacity, binding number,scattering number, and integrity, were presented to assess the vulnerability ofnetworks. Calculating the values of these vulnerability parameters can be challenging,particularly for certain classes of graphs, such as generalized Petersengraphs, due to their diverse structures. This paper establishes upper and lowerbounds for the tenacity of generalized Petersen graphs. We demonstrate a lowerbound of 1 for the tenacity, T (GPG(n, k)), across all values of n and k. Additionally,we explore the tenacity values of generalized Petersen graphs and presenta general upper bound for the tenacity value in this graph type. By using therelationship between the tenacity parameter and the connectivity (κ) and toughness(t) parameters, we also update some theorems related to the connectivityand toughness of generalized Petersen graphs.