On additive vertex labelings

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>In a quite general sense, additive vertex labelings are those functions that assign nonnegative integers to the vertices of a graph and the weight of each edge is obtained by adding the labels of its end-vertices. In this work we study one of these functions, called harmonious labeling. We calculate the number of non-isomorphic harmoniously labeled graphs with <em>n</em> edges and at most </span><span>n </span><span>vertices. We present harmonious labelings for some families of graphs that include certain unicyclic graphs obtained via the corona product. In addition, we prove that all <em>n</em>-cell snake polyiamonds are harmonious; this type of graph is obtained via edge amalgamation of n copies of the cycle <em>C</em>₃ in such a way that each copy of this cycle shares at most two edges with other copies. Moreover, we use the edge-switching technique on the cycle <em>C</em>_4<em>t</em>to generate unicyclic graphs with another type of additive vertex labeling, called strongly felicitous, which has a solid bond with the harmonious labeling.</span></p></div></div></div>