Title: Domination number of complete restrained fuzzy graphs

Authors: R. Jahir Hussain; S. Satham Hussain; Sankar Sahoo; Madhumangal Pal

Addresses: Department of Mathematics, Jamal Mohamed College, Trichy, 620 020, Tamil Nadu, India ' Department of Mathematics, Jamal Mohamed College, Trichy, 620 020, Tamil Nadu, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India ' Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721 102, India

Abstract: This work is concerned with the restrained complete domination number and triple connected domination number of fuzzy graphs. Some basic definitions and needful results are given with an example. The necessary and sufficient conditions for the fuzzy graph to be a complete restrained domination set is formulated and proved. Also the relation between complete restrained domination set and n-dominated set is illustrated. Finally, triple connected domination number of a restrained complete fuzzy graph is provided.

Keywords: fuzzy graphs; complete restrained domination set; complete restrained domination number; triple connected domination number.

DOI: 10.1504/IJAIP.2023.128073

International Journal of Advanced Intelligence Paradigms, 2023 Vol.24 No.1/2, pp.38 - 48

Received: 10 Nov 2017
Accepted: 23 Nov 2017
Published online: 05 Jan 2023 *