Interval-valued bipolar fuzzy line graphs

• Published in: BMC research notes Vol. 16; no. 1; p. 118
• Main Authors: Tola, Keneni Abera, Repalle, V N Srinivasa Rao, Ashebo, Mamo Abebe
• Format: Journal Article
• Language: English
• Published: England BioMed Central Ltd 26-06-2023; BioMed Central; BMC
• Subjects: Analysis; Bipolar fuzzy graph; Decision making; Fuzzy algorithms; Fuzzy Logic; Fuzzy sets; Fuzzy systems; Graph theory; Graphs; Humans; Interval-valued bipolar fuzzy graph Isomorphism; Interval-valued bipolar fuzzy line graph; Models, Theoretical; Research Note; Ethiopia; Interval-valued bipolar fuzzy line graph; Bipolar fuzzy graph; Interval-valued bipolar fuzzy graph Isomorphism
• ISSN: 1756-0500; 1756-0500
• DOI: 10.1186/s13104-023-06352-9

The notion of Bipolarity based on positive and negative outcomes. It is well known that bipolar models give more precision, flexibility, and compatibility to the system as compared to the classical models and fuzzy models. A bipolar fuzzy graph(BFG) provides more flexibility while modeling human thinking as compared with a fuzzy graph, and an interval valued bipolar fuzzy graph(IVBFG) has numerous applications where the real-life problem are time dependent and there is a network structure complexity. The aim of this paper is to introduce an interval-valued bipolar line fuzzy graph(IVBFLG).
In this paper, we have proposed the notion of an IVBFLG and some of its characterizations. Also, some propositions and theorems related to an IVIFLGs are developed and proved. Furthermore, isomorphism between two IVIFLGs toward their IVIFGs was determined and verified. As a result, we derive a necessary and sufficient condition for an IVBFG to be isomorphic to its corresponding IVBFLG and some remarkable properties like degree, size, order, regularity, strength, and completeness of an IVBFLGs have been investigated, and the proposed concepts are illustrated with the examples.