Connected Restrained Detour Number of a Graph

G Priscilla Pacifica; K Christy Rani; S Sethu Ramalingam

doi:10.17485/IJST/v16i1.1875

Article

Connected Restrained Detour Number of a Graph

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i1.1875

Year: 2023, Volume: 16, Issue: 1, Pages: 32-36

Original Article

Connected Restrained Detour Number of a Graph

G Priscilla Pacifica¹, K Christy Rani^2*, S Sethu Ramalingam³

¹Department of Mathematics, St. Mary’s College (Autonomous), Thoothukudi, 628001, India
²Reg. No.: 20122212092002, PG and Research Department of Mathematics, St. Mary’s College (Autonomous),Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, 627012, India
³Department of Mathematics, St. Xavier’s College (Autonomous), Palayamkottai , 627002, India

*Corresponding Author
Email: [email protected]

Received Date:17 October 2022, Accepted Date:30 October 2022, Published Date:05 January 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

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

Copyright

© 2022 Pacifica et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)