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

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

Journal of Applied Mathematics, 2013, vol. 2013, issue 1

Abstract: 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), xy ∈ E(G), form an arithmetic progression starting from a and having a common difference d, where a > 0 and d ≥ 0 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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2013:y:2013:i:1:n:896815

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