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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.
05C78 Graph labelling (graceful graphs, bandwidth, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)