On the Flower Graph Related to the Difference Square Mean Fuzzy Labeling

Abstract

Label learning is a fundamental task in machine learning that aims to construct intelligent models using labeled data, encompassing traditional single-label and multi-label classification models. Traditional methods typically rely on logical labels, such as binary indicators (e.g., "yes/no") that specify whether an instance belongs to a given category. The present research uses the difference square mean fuzzy values of neighboring vertices to construct an integrated fuzzy edge-labeling strategy for unpredictable graph architectures. Four structurally different graphs are subjected to the suggested fuzzy edge labeling. Rose flowers, sunflower, lily flowers, and Ammi Majus graphs are flower families. The explicit edge-labeling processes are generated for each category, and a series of theorems and examples are used to show the existence and consistency of the Difference Square Mean Fuzzy labeling (DSMFL). The findings demonstrate that all four graphs have distinctive replication processes controlled by their structural characteristics and accept the suggested fuzzy labeling. A compressed analytical method for analyzing fuzzy edge labeling in various and unpredictable network components is presented in this article.