Modelling Networks with Attached Storage Using Perfect Italian Domination

Abstract

Network-attached storage (NAS) is how data is stored and shared among hosts through a configured network. This is cheaper yet the best solution for sharing and using any huge unstructured data in an organization. Optimal distribution of NAS in a network of servers can be done using the concept of Perfect Italian Domination (PID). PID is a vertex labelling where the vertices of a graph G are labelled by 0, 1, 2 such that a vertex with label 0 should have a neighbourhood where the summation of the labels is exactly 2. The minimum possible sum of the labels obtained for graph G is its PID number. A network in an organization can have any structure. It can be highly interconnected, like a graph obtained from the Join of two graphs or the Corona product of two graphs. Hence, this paper discusses the PID of different graphs generated by the Join and the Corona products.