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Some new bounds for edge-magic graphs. (English) Zbl 1293.05331
Summary: We construct new bounds for the edge-magic index of a graph $$G$$. In particular, if $$G$$ is a $$(p,q)$$ graph in Vizing class 1 with $$r\mid p$$, we show that the edge-magic index of $$G$$ is at most $$p/r$$. If $$G$$ is an edge-magic graph with longest induced path of length $$\ell$$, we show that $$q\geq{p(\ell-1)\over 2}+ 1$$. We also produce a simplified means of testing if a graph is edge-magic and discuss the $$\text{Mod}(k)$$ edge-magic problem for $$r$$-regular graphs.
##### MSC:
 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)