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All Journal Jurnal Matematika UNAND Makara Journal of Science
Sugeng, Kiki A
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Computer Science & IT Mathematics

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SUPER EDGE MAGIC TOTAL LABELING ON UNICYCLIC GRAPHS Sepang, Adidarma; Wibowo, P. Anton; Herawati, Bong Bong; Sugeng, Kiki A
Makara Journal of Science Vol. 12, No. 1
Publisher : UI Scholars Hub

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Abstract

Let G = (V,E) be a simple, connected and undirected graph with v vertices and e edges. An edge magic total labeling is a bijection f from V∪E to a set of integers {1,2,…,v+e} such that if xy is an edge of G then the weight of edge f(x)+f(y)+f(xy) = k, for some integer constant k. A super edge magic total labeling is an edge magic total labeling f which f(V) = {1, · · · , v}. In this paper we construct new super edge magic total labeling of special classes of unicyclic that we construct from a super edge magic total labeling of odd cycles. Our construction uses embedding process of odd cycles, which is labeled by edge magic total labeling to grid, and uses edge transformation to obtain interesting new classes of super edge magic total unicyclic graphs.
The THE LOCAL ANTIMAGIC TOTAL CHROMATIC NUMBERS ON BARBELL WHEEL GRAPHS Sugeng, Kiki A; M. Fachriza, Evan
Jurnal Matematika UNAND Vol. 14 No. 3 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.3.267-274.2025

Abstract

\textbf{Abstract}. % Dalam bahasa Inggris \textit{Let $G=(V,e)$ be a graph with a finite non-empty vertex set $V(G)$ and a edge set $E(G)$. A local antimagic total labeling on graph $G$ defined as a bijective mapping $f$ from a union of the vertex set and the edges set of $G$ to a set of integers $\{1,2,\dots,|V(G)|+|E(G)|\}$ such as for all two adjacent vertices $u$ and $v$ we have $w_t(u)\neq w_t(v)$, where $w_t(u)=f(u)+\sum_{e\in E(u)}{f(e)}$ is a weight of vertex $u$, and $E(u)$ is a set of adjacent edges on the vertex $u$. Each distinct vertex weight in local antimagic total labeling can be considered as distinct colors, so that local antimagic total labeling on graph $G$ induces vertex coloring on graph $G$, with minimum numbers of colors or its chromatic number denoted as $\chi_{lat}(G)$. The barbell wheel graph $BW_{n,k}$, with $n\geq3$ and $k\geq2$, is defined as a graph with two subgraphs of wheels $W_n$ that are connected by the path subgraph $P_k$ at each center vertex. In this paper, we prove that the barbell wheel graph $BW_{n,k}$ has local antimagic total labeling. We also determine its local antimagic total chromatic number.}\\
Co-Authors Herawati, Bong Bong M. Fachriza, Evan Sepang, Adidarma Wibowo, P. Anton