Objectives: To find the connected restrained detour number for standard graphs and mesh graphs. Methods: By determining set with minimum cardinality, of a graph is investigated. Findings: We study that altered when we add pendent vertices. The maximum degree vertices are deleted computed. Novelty: Finding path plays vital role in network-based systems. Planning largest route essential business,...

Let G be a simple non-complete graph of order n. The r-component edge connectivity of G denoted as λr(G) is the minimum number of edges that must be removed from G in order to obtain a graph with (at least) r connected components. The concept of r-component edge connectivity generalizes that of edge connectivity by taking into account the number of components of the resulting graph. In this pap...