Journal of Applied Mathematics

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

Abstract

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

Article information

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

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808051

Digital Object Identifier
doi:10.1155/2013/896815

Mathematical Reviews number (MathSciNet)
MR3074334

Zentralblatt MATH identifier
1271.05087

Citation

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. https://projecteuclid.org/euclid.jam/1394808051

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