Abstract
Objectives: To find the connected restrained detour number for standard graphs and mesh graphs. Methods: By determining the connected restrained detour set with minimum cardinality, the connected restrained detour number of a graph is investigated. Findings: We study that the connected restrained detour number of the graphs is altered when we add pendent vertices. The minimum and maximum degree vertices of a graph are deleted and the connected restrained detour number of the mesh graph is computed. Novelty: Finding the detour path plays a vital role in the network-based systems. Planning the largest route that is connected and restrained is essential in business, industries and radio technologies. We introduce the new concept of connected restrained detour number. We also exhibit the bounds for the connected restrained detour set of a graph. Keywords: Detour Set; Detour Number; Mesh Graphs; Connected Restrained Detour Set; Connected Restrained Detour Number
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