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Agnes Ika Nurvitaningrum, Agnes Ika
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Education Mathematics

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Pelabelan Total Super (a,d)-Sisi Antimagic Pada Graf Buah Naga Nurvitaningrum, Agnes Ika; Dafik, Dafik; Setiawani, Susi
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 $G$ is called an $(a,d)$-edge-antimagic total labeling if there exist a one-to-one mapping $f : f(V)={1,2,3,...,p} o f(E)={1,2,dots,p+q}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv in E(G)$, form an arithmetic progression ${a,a+d,a+2d,dots,a+(q-1)d}$, where $a>0$ and $dge 0$ are two fixed integers, form an arithmetic sequence with 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 recite super $(a,d)$-edge-antimagic total labelling of connected  Dragon Fruit Graph. The result shows that Dragon Fruit Graph have a super edge antimagic total  labeling for $din{0,1,2}$.
Pelabelan Total Super (a,d)-Sisi Antimagic Pada Graf Buah Naga Nurvitaningrum, Agnes Ika; Dafik, Dafik; Setiawani, Susi
Prosiding Seminar Matematika dan Pendidikan Matematik Vol 1 No 5 (2014): Prosiding Seminar Nasional Matematika 2014
Publisher : Prosiding Seminar Matematika dan Pendidikan Matematik

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

A graph $G$ is called an $(a,d)$-edge-antimagic total labeling if there exist a one-to-one mapping $f : f(V)=\{1,2,3,...,p\} \to f(E)=\{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic progression $\{a,a+d,a+2d,\dots,a+(q-1)d\}$, where $a>0$ and $d\ge 0$ are two fixed integers, form an arithmetic sequence with 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 recite super $(a,d)$-edge-antimagic total labelling of connected  Dragon Fruit Graph. The result shows that Dragon Fruit Graph have a super edge antimagic total  labeling for $d\in{0,1,2}$.
Co-Authors D. Dafik Susi Setiawani