Prime Labeling of Rough Approximations for Some Special Graphs

Background/Objectives: Rough set theory proposed a new mathematical approach to vagueness or imperfect knowledge. It is the learning of approximations of concepts represented by lower and upper approximations which is being attracted by many researchers. The current study is a combination of rough sets approximation and graph labeling. Methods/Analysis: Many researchers have studied prime graph. Here we combine rough approximations with prime labeling under the name of H-prime labeling on graph G. Findings: The current work is to prove that the induced sub graph obtained by the upper approximation of any sub graph H of a friendship graph F_n, bistar graph B_n,n and splitting graph of a star graph 'S' ' graph admits prime labeling. The various applications between rough sets and graph labeling are chemical classification, decision analysis, knowledge acquisition, machine learning, job assignment etc.