Journal of Applied Mathematics

On Super (a,d)-Edge-Antimagic Total Labeling of Special Types of Crown Graphs

Himayat Ullah, Gohar Ali, Murtaza Ali, and Andrea Semaničová-Feňovčíková

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For a graph G=(V,E), a bijection f from V(G)E(G){1,2,,|V(G)|+|E(G)|} is called (a,d)-edge-antimagic total ((a,d)-EAT) labeling of G if the edge-weights w(xy)=f(x)+f(y)+f(xy),xyE(G), form an arithmetic progression starting from a and having a common difference d, where a>0 and d0 are two fixed integers. An (a,d)-EAT labeling is called super (a,d)-EAT labeling if the vertices are labeled with the smallest possible numbers; that is, f(V)={1,2,,|V(G)|}. In this paper, we study super (a,d)-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle.

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J. Appl. Math., Volume 2013 (2013), Article ID 896815, 6 pages.

First available in Project Euclid: 14 March 2014

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Ullah, Himayat; Ali, Gohar; Ali, Murtaza; Semaničová-Feňovčíková, Andrea. On Super $\left(a,d\right)$ -Edge-Antimagic Total Labeling of Special Types of Crown Graphs. J. Appl. Math. 2013 (2013), Article ID 896815, 6 pages. doi:10.1155/2013/896815.

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