Robustness in Mesh Networks Using Connected Safe Set and Applications

The robustness of the networks is their capacity to remain operational in the presence of faults and disruptions, and thereby it is an important tool to provide data transmission in telecommunications networks such as wireless networks, enterprise networks, and cloud computing networks. The 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). The least size of CSS is known as connected safe number (CSN). The identification of the connected collection of nodes in the networks, capable of enduring dual load in case of faults and disruption, can be realized as CSS. Mesh networks (MNs) have become an integral part of a variety of domains, such as smart cities, disaster recovery, Internet of Things (IoT) and military defense, due to their decentralized nature and ability to reconfigure as conditions change dynamically. In this paper, the CSS and CSN for various types of MNs, such as triangular, triangular circular, double triangular circular, and quadrangular necklace mesh are computed. Finally, an application of CSS in the context of optimal router installation on certain MNs is included.