摘要：A graph G(p,q) is said to have an edge-magic totallabeling if there exists a bijective function f: V (G) ∪ E(G) →{1,2,··· ,p+q}, such that for any edge uv of G, f(u)+f(v)+f(uv) = k, k is a constant. Moreover, G is said to have asuper edge-magic total labeling if f(V (G)) = {1,2,··· ,p}.We propose a new algorithm, based on the graph generationmethod, to solve the problem of super edge-magic total labelingof graphs with a large number of vertices. First, we introduce anew operation called generalized coalescence, then we generatethe adjacent matrices of graphs composed of fans, circle andstar. Second, we input these matrices to our proposed algorithm.Third, if a graph exist a super edge-magic total labeling, thealgorithm will output the corresponding super edge-magic totallabeling matrices. Otherwise, no super edge-magic total labelingexists for the graphs involved. Fourth, from the results, weconclude that regular labels are found in some of the graphsinvolved. Our algorithm can distinguish super edge-magic totallabeling graphs from those graphs which don’t have.
关键词：super edge-magic total labeling; algorithm; graphs
