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Wicha Dwi Vikade, Wicha Dwi
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Education Mathematics

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Super (a,d)-Edge-antimagic Total Labeling of Shakle of Fan Graph Vikade, Wicha Dwi; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1, No 1 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

A graph $G$ of order $p$ and size $q$ is called an {it $(a,d)$-edge-antimagic total} if there exist a bijection $f : V(G)cup E(G) o {1,2,dots,p+q}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv in E(G)$, form an arithmetic sequencewith first term $a$ and common difference $d$. Such a graph $G$ is called {it super} if the smallest possible labels appear on the vertices. In this paper we study super $(a,d)$-edge-antimagic total properties of connected  of amalgamation of Fan Graph. The result shows that amalgamation of Fan Graph admit a super edge antimagic total labeling for $din{0,1,2}$ for $n$ $geq$ 1. It can be concluded that the result of this research has convered all the feasible $n$, $d$.
Super (a,d)-Edge-antimagic Total Labeling of Shakle of Fan Graph Vikade, Wicha Dwi; Dafik, Dafik
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

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Abstract

A graph $G$ of order $p$ and size $q$ is called an {\it $(a,d)$-edge-antimagic total} if there exist a bijection $f : V(G)\cup E(G) \to \{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic sequencewith first term $a$ and common difference $d$. Such a graph $G$ is called {\it super} if the smallest possible labels appear on the vertices. In this paper we study super $(a,d)$-edge-antimagic total properties of connected  of amalgamation of Fan Graph. The result shows that amalgamation of Fan Graph admit a super edge antimagic total labeling for $d\in{0,1,2}$ for $n$ $\geq$ 1. It can be concluded that the result of this research has convered all the feasible $n$, $d$.
Co-Authors D. Dafik