Even vertex $ζ$-graceful labeling on Rough Graph
This work provides a new labeling method for rough graphs, which are used in information systems with imprecise knowledge, but it appears incremental as it builds directly on existing rough graph concepts.
The paper introduces Even vertex ζ-graceful labeling as a new type of edge weight labeling for rough graphs, which model information systems with imprecise knowledge, and investigates this labeling for specific rough graph structures like path, cycle, comb, ladder, and star graphs.
Rough graph is the graphical structure of information system with imprecise knowledge. Tong He designed the properties of rough graph in 2006[6] and following that He and Shi introduced the notion of edge rough graph[7]. He et al developed the concept of weighted rough graph with weighted attributes[6]. In this paper, we introduce a new type of labeling called Even vertex ζ- graceful labeling as weight value for edges. We investigate this labeling for some special graphs like rough path graph, rough cycle graph, rough comb graph, rough ladder graph and rough star graph.