Computing the weighted neighbor isolated tenacity of interval graphs in polynomial time

Weighted graphs in graph theory are created by weighing different values depending on the importance of connections or centers in a graph model. Networks can be modeled with graphs such that the devices and centers correspond to the vertices and connections correspond to the edges. In these networks, weight can be assigned to the vertices for the workload and importance of the devices and centers, so that planning such as security and cost can be made in advance in the design of the network. Network reliability and security is an important issue in the computing area. There are several parameters for vulnerability measurement values of these networks modeled with graphs. We recommend the weighted conversion of the neighbor isolated tenacity parameter for this topic. It is known that tenacity, which is the basis of this parameter, is NP‐hard. But polynomial solutions can be created in interval graphs, which is a special graph from the perfect graph class. In this article, polynomial time algorithm is given to calculate weighted neighbor isolated tenacity of the interval graphs.