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Even vertex $ζ$-graceful labeling on Rough Graph

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.