Super edge-antimagic graceful labeling of graphs
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https://doi.org/10.26637/mjm303/010Abstract
For a graph \(G=(V, E)\), a bijection \(g\) from \(V(G) \cup E(G)\) into \(\{1,2, \ldots,|V(G)|+|E(G)|\}\) is called \((a, d)\)-edge-antimagic graceful labeling of \(G\) if the edge-weights \(w(x y)=|g(x)+g(y)-g(x y)|, x y \in E(G)\), form an arithmetic progression starting from \(a\) and having a common difference \(d\). An \((a, d)\)-edge-antimagic graceful labeling is called super \((a, d)\)-edge-antimagic graceful if \(g(V(G))=\{1,2, \ldots,|V(G)|\}\). Note that the notion of super \((a, d)\)-edge-antimagic graceful graphs is a generalization of the article "G. Marimuthu and \(\mathrm{M}\). Balakrishnan, Super edge magic graceful graphs, Inf.Sci.287( 2014)140-151", since super \((a, 0)\)-edge-antimagic graceful graph is a super edge magic graceful graph.We study super \((a, d)\)-edge-antimagic graceful properties of certain classes of graphs, including complete graphs and complete bipartite graphs.
Keywords:
Edge-antimagic graceful labeling, Super edge-antimagic graceful labelingMathematics Subject Classification:
05C78- Pages: 312-317
- Date Published: 01-07-2015
- Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)
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