A new algorithm to accurately determine whether a graph has a super edge-magic total labeling or not

Abstract

We propose a new algorithm, based on the graph generation method, to solve the problem of super edge-magic total labeling of graphs with a large number of vertices. Our main contributions to solving the graph labeling problem are: first, we generate the adjacent matrices of graphs composed of fans and stars. Second, we input these matrices to our proposed algorithm. Third, if the labeling is successful, the algorithm will output the corresponding super edge-magic total labeling matrices. Otherwise, no super edge-magic total labeling exists for the graphs involved. Forth, through the analysis of the results obtained by our algorithm, we conclude that regular labels are found in some of the graphs involved. Our algorithm can distinguish between graphs that have a super edge-magic total labeling and graphs that don't efficiently. We think that our proposed algorithm is innovative and can be adopted by other researchers.