Enumerating Families of Labeled Graphs
نویسندگان
چکیده
In 1966, Rosa introduced, among others, αand β-labelings as tools to solve the isomorphic decomposition problem of the complete graph. Ten years later, Sheppard calculated the number of αand β-labeled graphs with n edges. In this paper we use an extended version of the adjacency matrix of a graph to determine the number of gracefully labeled graphs with n edges; furthermore, we also calculate the number of them withm vertices for every suitable value ofm. In addition, we use this technique to determine the number of labeled graphs for other types of labelings as the harmonious, felicitous, and elegant.
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