Even Vertex <img src=image/13429275_01.gif>-Graceful Labeling on Rough Graph

Abstract

The study of set of objects with imprecise knowledge and vague information is known as rough set theory. The diagrammatic representation of this type of information may be handled through graphs for better decision making. Tong He and K. Shi introduced the constructional processes of rough graph in 2006 followed by the notion of edge rough graph. They constructed rough graph through set approximations called upper and lower approximations. He et al developed the concept of weighted rough graph with weighted attributes. Labelling is the process of making the graph into a more sensible way. In this process, integers are assigned for vertices of a graph so that we will be getting distinct weights for edges. Weight of an edge brings the degree of relationship between vertices. In this paper we have considered the rough graph constructed through rough membership values and as well as envisaged a novel type of labeling called Even vertex <img src=image/13429275_02.gif>-graceful labeling as weight value for edges. In case of rough graph, weight of an edge will identify the consistent attribute even though the information system is imprecise. We have investigated this labeling for some special graphs like rough path graph, rough cycle graph, rough comb graph, rough ladder graph and rough star graph etc. This Even vertex <img src=image/13429275_02.gif>-graceful labeling will be useful in feature extraction process and it leads to graph mining.