Intuitionistic fuzzy graphs of n^th type with applications

Article type: Research Article

Authors: Davvaz, Bijan^a | Jan, Naeem^b | Mahmood, Tahir^b | Ullah, Kifayat^{b; *}

Affiliations: [a] Department of Mathematics, Yazd University, Yazd, Iran | [b] Department of Mathematics and Statistics, International Islamic University Islamabad Pakistan

Correspondence: [*] Corresponding author. Kifayat Ullah, Department of Mathematics and Statistics, International Islamic University Islamabad Pakistan. Tel.: +92 334 9090225; E-mail: kifayat.phdma72@iiu.edu.pk.

Abstract: In this article, a new concept of intuitionistic fuzzy graph of nth type (IFGNT) is proposed as a generalization of intuitionistic fuzzy graphs (IFGs) and intuitionistic fuzzy graphs of second type (IFGST). Some light has also been shed upon the concepts of constant intuitionistic fuzzy graphs of second type (CIFGST) and constant intuitionistic fuzzy graphs of nth type (CIFGNT). Moreover, some basic definitions of and results from IFGNT have been developed, supported with examples. Besides, the advantages of proposed new concept over the existing concepts have been highlighted and a comparative study of new and existing works made. Further, an application of IFGNT has been demonstrated in social networks context.

Keywords: Intuitionistic fuzzy graphs, intuitionistic fuzzy graphs of second type, intuitionistic fuzzy graphs of n-type, constant intuitionistic fuzzy graphs of second type, constant intuitionistic fuzzy graphs of n-type, social networks

DOI: 10.3233/JIFS-181123

Journal: Journal of Intelligent & Fuzzy Systems, vol. 36, no. 4, pp. 3923-3932, 2019