Abstract
Harmonious labelings are very important in the literature, since many authors have devoted their efforts to better understanding them. Thus, we believe that it is worth the while to dedicate special attention to them. However many of the results that involve harmonious labelings can be obtained using similar ideas to the ones used for super edge-magic labelings as well as using the relations that appear in Sects. 3.1 and 6.3 Therefore, we will dedicate only a short chapter to this important labeling. We start answering the question of which complete graphs are harmonious. Later we will study a few families of harmonious graphs as well as general properties of these graphs. We will conclude this chapter providing an asymptotic answer to the question of how many graphs are harmonious.
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López, S.C., Muntaner-Batle, F.A. (2017). Harmonious Labelings. In: Graceful, Harmonious and Magic Type Labelings. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-52657-7_4
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DOI: https://doi.org/10.1007/978-3-319-52657-7_4
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