Super Edge-antimagic Graceful labeling of Graphs

G. Marimuthua,* and P. Krishnavenib

Super Edge-antimagic Graceful labeling of Graphs

Authors :

G. Marimuthu^a,* and P. Krishnaveni^b

Author Address :

^a,bDepartment of Mathematics, The Madura College, Madurai–625011, Tamil Nadu, India.

*Corresponding author.

Abstract :

For a graph $G = (V,E),$ a bijection $g$ from $V(G)\cup E(G)$ into $\{1,2,\dots,|V(G)|+|E(G)|\}$ is called $(a,d)$-edge-antimagic graceful labeling of $G$ if the edge-weights $ w(xy)=|g (x) + g (y)-g (xy)|, xy\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 $g (V(G)) = \{ 1,2,\dots,|V(G)|\}.$ Note that the notion of super $(a,d)$-edge-antimagic graceful graphs is a generalization of the article ``G. Marimuthu and 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.