An algorithmic approach to signed fuzzy graph integrity: Complexity, graph operations, and metro rail network applications

Abstract

This paper presents an algorithm to compute the integrity of a signed fuzzy graph by systematically evaluating vertex subsets, removing them, and analyzing the resulting connected components. Integrity is determined by computing the minimum sum of the fuzzy membership of the removed subset and the maximum fuzzy order among the remaining components. Additionally, this study explores the vertex integrity of signed fuzzy graphs under operations such as union, Cartesian product, and join. Integrity results for special graph operations are derived and illustrated with examples. The corona and pendant operations on signed fuzzy graphs are also introduced, along with their structural properties. Understanding graph integrity is essential for assessing network resilience, particularly in transportation systems. The proposed framework is applied to metro rail networks to demonstrate its practical significance in ensuring operational efficiency. Integrity values are computed using computational tools, providing insights into network robustness and failure resilience.

Keywords

• Signed fuzzy graph (signed-FG)
• Corona of signed fuzzy graph
• Pendant signed fuzzy graph