As many readers may know, graph theory is a fundamental branch of mathematics that
examines networks consisting of nodes and edges, with a focus on their paths, structures …

Graph theory is a fundamental branch of mathematics that examines networks composed of
nodes (vertices) and connections (edges). This paper explores the concepts of permutation …

In this manuscript, we introduce the notion of interval-valued picture (S, T)-fuzzy graphs (IVP-
(S, T)-fuzzy graphs) which is the interplay between (S, T)-norms and picture fuzzy graphs …

The connectivity index (CI), Wiener index (WI), and Randic index (RI) play a significant role
in modeling various problems such as networking, transportation, and precise location …

Fuzzy graphs, including their extensions such as intuitionistic fuzzy graphs and picture fuzzy
graphs, find substantial applications in diverse natural and human-made systems. The …

In the realm of handling imprecise information, picture fuzzy cubic sets have emerged as a
more versatile tool compared to cubic sets, cubic intuitionistic fuzzy sets, and similar models …

The idea of strong and weak adjacencies between vertices has been generalized into fuzzy
graphs and intuitionistic fuzzy graphs (IFGs), and it is an important part of making decisions …

Group decision-making is a technique wherein professionals rank and select the most
acceptable ones based on recognised criteria. The objective of the present study was to …

Nowadays in reality there are a lot of uncertainties and it is well-known that fuzzy graphs can
efficiently handle such a situation. Picture fuzzy graph is a generalization of fuzzy graph and …

This study focuses on forming planar subgraphs in fuzzy graphs where the planarity value is
not equal to 1. The paper commences by introducing the concepts of vertex-deletion (VD) …