Even vertex $\zeta$-graceful labeling on Rough Graph

TL;DR

This paper introduces a new labeling method called Even vertex ζ-graceful labeling for rough graphs, analyzing its properties on various special graph structures to enhance understanding of graph labelings in imprecise information systems.

Contribution

The paper proposes a novel Even vertex ζ-graceful labeling for rough graphs and explores its application on several specific graph types, expanding the theory of graph labelings.

Findings

Defined Even vertex ζ-graceful labeling for rough graphs.

Applied the labeling to rough path, cycle, comb, ladder, and star graphs.

Provided initial results on the existence of such labelings for these graphs.

Abstract

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 {\zeta}- 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.