Intuitionistic Fuzzy Planar Graphs

Abstract

Graph theory has numerous applications in modern sciences and technology. Atanassov introduced the concept of intuitionistic fuzzy sets as a generalization of fuzzy sets. Intuitionistic fuzzy set has shown advantages in handling vagueness and uncertainty compared to fuzzy set. In this paper, we apply the concept of intuitionistic fuzzy sets to multigraphs, planar graphs, and dual graphs. We introduce the notions of intuitionistic fuzzy multigraphs, intuitionistic fuzzy planar graphs, and intuitionistic fuzzy dual graphs and investigate some of their interesting properties. We also study isomorphism between intuitionistic fuzzy planar graphs.

Single-valued Neutrosophic planar graphs

“…We present some of their interesting properties. This paper is a continuation of Alshehri and Akram's work [10].…”

“…Samanta and Pal [17,19] introduced and investigated the concept of fuzzy planar graphs and studied several properties. On other hand, Alshehri and Akram [10] introduced the concept of intuitionistic fuzzy planar graphs. Akram et al [5] discussed the concept of bipolar fuzzy planar graphs.…”

Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies

“…Shannon and Atanassov [22] and Akram and Davvaz [23] defined intuitionistic fuzzy graphs. Later, several authors worked on intuitionistic fuzzy graphs and added many useful results to this area, for instance, Akram and Akmal [24], Alshehri and Akram [25], Karunambigai et al [26], Myithili et al [27], Nagoorgani et al [28] and Parvathi et al [29,30]. See also [31][32][33][34][35].…”

Planar Graphs under Pythagorean Fuzzy Environment

“…Pramanik et al [3] discussed special planar fuzzy graphs. Furthermore, some extensions of planar fuzzy graph were studied [28][29][30]. For other terminologies and applications, one can see [31][32][33][34][35][36][37].…”