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All Journal Jurnal Matematika & Sains Indonesian Journal of Combinatorics
Denny Riama Silaban
Universitas Indonesia
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics

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Vertex-Magic Total Labeling Algorithms on Unicycle Graphs and Some Graphs Related to Wheels Denny Riama Silaban; Budi Utami; Alfa Isti Ananda; Dhian Widya; Siti Aminah
Jurnal Matematika & Sains Vol 17, No 1 (2012)
Publisher : Institut Teknologi Bandung

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Abstract

Abstract Let G be a graph with vertex set V and edge set E, where |V| and |E| be the number of vertices and edges of G. A bijection λ : V È E ® {1, 2, …, |V| + |E|} is called a vertex-magic total labeling if there is a constant k so that the weight of vertex x, wλ(x) = λ(x) + åyÎN(x) λ(xy) = k, for all x in V where N(x) is the set of vertices adjacent to x. This paper gives algorithms to generate all vertex-magic total labelings on some classes of unicycle graphs (suns and tadpoles) and some classes of graph related to wheels (friendships, fans, generalized Jahangirs). Using those algorithms, we enumerate all non isomorphic vertex-magic total labelings on those classes of graphs for some values of |V|.   Keywords: Fan, Friendship, Generalized Jahangir, Sun, Tadpole, Unicycle, Vertex magic total labeling, Wheel.   Algoritma Pelabelan Total Simpul Ajaib pada Graf Unicyle dan Beberapa Graf yang Terkait dengan Roda Abstrak Misalkan G adalah graf dengan himpunan simpul V dan himpunan busur  E dengan |V| dan |E| menyatakan banyak simpul dan banyak busur pada G. Fungsi bijektif  λ : V È E ® {1, 2, …, |V| + |E|} disebut pelabelan total simpul ajaib jika ada konstanta k sedemikian sehingga bobot simpul x, wλ(x) = λ(x) + åyÎN(x) λ(xy) = k, untuk setiap x di V dengan N(x) menyatakan, himpunan simpul yang berdekatan dengan x. Makalah ini memberikan algoritma-algoritma untuk menghasikan semua pelabelan-pelabelan  total simpul ajaib pada beberapa kelas graf unicycle (matahari dan kecebong) dan beberapa kelas graf yang terkait dengan roda (friendship, kipas, generalized Jahangir). Menggunakan algoritma-algoritma tersebut, dienumerasi semua pelabelan total simpul ajaib yang tidak isomorfik pada kelas-kelas graf yang menjadi perhatian, untuk beberapa nilai dari |V|. Kata kunci: Friendship, Generalized Jahangir, Kecebong, Kipas, Matahari, Pelabelan total simpul ajaib, Unicycle. 
Super local edge anti-magic total coloring of paths and its derivation Fawwaz Fakhrurrozi Hadiputra; Denny Riama Silaban; Tita Khalis Maryati
Indonesian Journal of Combinatorics Vol 3, No 2 (2019)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (636.8 KB) | DOI: 10.19184/ijc.2019.3.2.6

Abstract

Suppose G(V,E) be a connected simple graph and suppose u,v,x be vertices of graph G. A bijection f : V ∪ E → {1,2,3,...,|V (G)| + |E(G)|} is called super local edge antimagic total labeling if for any adjacent edges uv and vx, w(uv) 6= w(vx), which w(uv) = f(u)+f(uv)+f(v) for every vertex u,v,x in G, and f(u) < f(e) for every vertex u and edge e ∈ E(G). Let γ(G) is the chromatic number of edge coloring of a graph G. By giving G a labeling of f, we denotes the minimum weight of edges needed in G as γleat(G). If every labels for vertices is smaller than its edges, then it is be considered γsleat(G). In this study, we proved the γ sleat of paths and its derivation.
Co-Authors Alfa Isti Ananda Bevina D Handari Budi Utami Dhian Widya Fawwaz Fakhrurrozi Hadiputra Joshita Djajadisastra Siti Aminah Tita Khalis Maryati