Title: Cayley bipolar fuzzy graphs associated with bipolar fuzzy groups

Authors: Ali Asghar Talebi; Samaneh Omidbakhsh Amiri

Addresses: Faculty of Mathematics, University of Mazandaran, Iran ' Faculty of Mathematics, University of Mazandaran, Iran

Abstract: Recently, bipolar fuzzy graph is a growing research topic as it is the generalisation of fuzzy graphs. Let G be a non-trivial group and S be a non-empty subset of G such that not containing the identity element of G and S = S^-1 = {s^-1| s ∈ S}. The Cayley graph Γ = Cay (G, S) is the graph whose vertex set V(Γ) is G and edge set E(Γ) is {{g, gs}| g ∈ G, s ∈ S}. A non-empty subset S of G such that not containing the identity and S = S^-1 is referred to as a Cayley subset of G, and the Cayley graph Γ = Cay (G, S) is referred to as a Cayley graph of G relative to S. In this paper, we introduce the concept of Cayley bipolar fuzzy graphs on the bipolar fuzzy groups. Also some properties of Cayley bipolar fuzzy graphs as connectivity and transitivity are provided.

Keywords: fuzzy graph; Cayley fuzzy graphs; bipolar fuzzy group; Cayley bipolar fuzzy graph; automorphism; isomorphism; level set; (s; t)-level set; level graph.

DOI: 10.1504/IJAIP.2023.128071

International Journal of Advanced Intelligence Paradigms, 2023 Vol.24 No.1/2, pp.1 - 11

Received: 11 Sep 2017
Accepted: 15 Oct 2017
Published online: 05 Jan 2023 *