Fuzzy Range Labeling of Fuzzy Star Graph and Helm Graph

Objectives: To find a new labeling technique in Fuzzy Graph Theory called Fuzzy Range Labeling. This concept helps to handle the uncertainty in graph labeling areas. Methods: Fuzzy graph labeling condition - and Range labeling condition - (that is, the edge membership value is calculated as the difference between the maximum and minimum values of the vertex incident to that edge) are used. Findings: In this study, we have found that the fuzzy star graph and helm graph are fuzzy range graphs. Novelty: The fuzzy range labeling technique was not yet studied. Thus, this new notion will motivate many researchers to study further. Keywords: Fuzzy graph labeling, Range labeling, Fuzzy range labeling, Fuzzy range graph, Fuzzy star graph, Helm graph