A study on various domination integrity parameters in graphs and fuzzy graphs

Abstract

Graph is one of the dynamic tools used to solve network-related newlineproblems and real-time application models. One of the main advantages of newlinegraphs is that a problem can be stated diagrammatically, which lead to a better newlinesolution. Connectivity is a crucial aspect in the field of graph theory. If a newlinecertain subset of vertices is removed, a graph may become disconnected and newlineform multiple connected components. It is important to establish a parameter newlinethat can link this vertex subset to the connected components. The essential newlinerequirements for every network are stability and reliability in terms of newlineconnectivity. Numerous vulnerabilities exist that can significantly impact the newlineperformance of a network. To quantify these vulnerabilities, the utilization of newlinea parameter becomes necessary. Graphs offer several vulnerability parameters newlinethat can be employed for this purpose. Two such parameters are strong newlinedomination integrity and geodetic domination integrity, which are defined newlinespecifically for graphs. newlineIn this thesis, the strong domination integrity values of various newlinetypes of graphs, such as the null graph, complete graph, path, cycle, star, newlinebipartite graph, Thron rod, Thron star and composition of two graphs are newlinecarefully listed. Also, the strong domination integrity value of corona-related newlinegraphs is calculated. newline