### On graphs with α- and *b*-edge consecutive edge magic labelings

#### Abstract

Among the most studied graph labelings we have the varieties called alpha and edge-magic. Even when their definitions seem completely different, these labelings are related. A graceful labeling of a bipartite graph is called an α-labeling if the smaller labels are assigned to vertices of the same stable set. An edge-magic labeling of a graph of size *n* is said to be *b*-edge consecutive when its edges are labeled with the integers *b+1*, *b+2*, ..., *b+n*, for some 0 ≤ *b* ≤ *n*. In this work, we prove the existence of several *b* edge-magic labelings for any graph of order *m* and size *m-1* that admits an α-labeling. In addition, we determine the exact value of *b* induced by the α-labeling, as well as for its reverse, complementary, and reverse complementary labelings.

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PDFDOI: http://dx.doi.org/10.19184/ijc.2022.6.1.4

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