Fermatean Neutrosophic Fuzzy Graphs: A Study on the Winner  Index with Enhancing Election Analysis

Wadei Fares AL-omeri; Kaviyarasu M; M. Rajeshwari

Authors

Wadei Fares AL-omeri Department of Mathematics, Faculty of Science and Information Technology Jadara University, Irbid, Jordan
Kaviyarasu M Department of Mathematics, Vel Tech Rangarajan Dr Sagunthala R & D Institute of Science and Technology, Chennai, Tamilnadu-600062, India;
M. Rajeshwari School of Engineering, Presidency University, Bangalure, India;

Keywords:

Fuzzy graph, FNG, Winner Index, Uncertainty Modeling, Decision Making

Abstract

In this article, we discuss the fermatean neutrosophic graph of Wiener index, which is an essential
topological index formed according to geodesical distance of vertices. The Wiener index is an important factor
to describe the structure of a graph and we de ned it in relation to fermatean neutrosophic graphs and computed
it for some speci c fermatean neutrosophic graph structures including complete fermatean neutrosophic graphs,
cycles and trees. Subsequently, the Wiener index is compared with the connectivity index, a core-degree
based parameter, using a sequence of theorems. As an application the study responds to the di culties in
election analysis in democratic environments where voter choices are often nuanced an unpredictable and the
methods of measurement are not sensitive enough to capture these changes. To improve the modeling of
election data, this work employs fermatean neutrosophic graphs (FNGs) and the Wiener index, which distinguish
nodes that represent leadership qualities, policy suggestions, and public commitment as well as the relationship
between these nodes. This approach manages uncertainty and indeterminacy well and provides a sound method
of enhancing the measurability and credibility of analytical techniques in managing complicated events like
elections.

DOI: 10.5281/zenodo.14707336