Co Secure Domination in Product Graphs and Interconnection Networks

Abstract

A mathematical abstraction of situations which focusses on the way in which the points newlineare connected together give rise to the concept called graph. This thesis examines a newlinefinite, un directed simple graph with no loops or multiple edges. newlineGraph theory provides a framework for representing interconnection networks as newlinesimple graph G = (V,E) where the network components are represented by vertices newlineand the connection links between them are depicted as edges. Physical security in newlinethe form of guards, cameras, and robots can be maintained at the critical positions newlinein the network to protect the network from unforeseen threats including natural and newlinehuman-made disasters. The strategical placement of mobile guards at particular vertices newlineof the network that secures a network forms a dominating set and the minimum newlinenumber of guards needed to protect the entire network is the domination number and#947;(G). newlineThe theory of Graph domination play a significant role in identifying the sensitive newlinelocations in a network where mobile guards have to be placed. Co-secure domination newline(CSD) provides an additional layer of protection to the network by replacing the physically weak or the attacked mobile guard stationed sensitive nodes with another guard so that the consequent set of guards continues to protect the network. newlineThis thesis proposes a general approach to protect graphs using co-secure domination. newlineThe minimum number of nodes that facilitates the designation of redundant newlinebackup nodes for critical components in a network is the co-secure domination number newlineand is denoted by and#947;cs(G). The co-secure domination number, and#947;cs(G) is analyzed in newlinevarious networks - Mycielski graphs, Generalized Mycielski graphs, Jump graphs..... newline newline