Title: Domination in hesitancy fuzzy graphs

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

Addresses: PG and Research Department of Mathematics, Jamal Mohamed College, Trichy – 620 020, Tamil Nadu, India ' PG and Research 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: Hesitant fuzzy sets (HFS) are introduced by author Torra which is a novel and recent extension of fuzzy sets that aims to model the uncertainty originated by the hesitation to arise in the assignment of membership degrees of the elements to a fuzzy set. Hesitancy fuzzy graphs (HFG) are introduced to capture the common intricacy that occurs during a selection of membership degree of an element from some possible values that makes one to hesitate. HFG are used to choose a time minimised emergency route (TiMER) to transport accident victims. This paper addresses the study of domination in hesitancy fuzzy graphs. By using the concept of strength of a path, strength of connectedness and strong arc, domination set is established. The necessary and sufficient condition for the minimum domination set of HFG is investigated. Further some properties of independent domination number of HFG are obtained and the proposed concepts are described with suitable examples.

Keywords: domination number; hesitancy fuzzy graphs; HFG; independent domination set; necessary and sufficient condition; strong arc.

DOI: 10.1504/IJAIP.2023.130812

International Journal of Advanced Intelligence Paradigms, 2023 Vol.25 No.1/2, pp.11 - 23

Received: 19 Dec 2017
Accepted: 03 Jan 2018
Published online: 11 May 2023 *

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