Computation of Connected Safe Set of Cycle-Related Networks and Applications

A connected collection of nodes in a network excluding which results in the decomposition of a network into components such that the cardinality of each component is at most equal to the cardinality of the collection is referred to as a connected safe set (CSS). A CSS of the least size is called connected safe basis and its cardinality is referred to as a connected safe number (CSN). In this article, we computed CSS and CSN of certain cycle-related networks, namely tadpole network, helm network, and prism network. In addition, we presented an application of the CSS for ensuring an optimal water distribution network in a smart city.