向日葵伞图的局部边(a, d) -反幻着色及其应用

R. Adawiyah, I. I. Makhfudloh, R. M. Prihandini
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摘要

假设图G = (V, E)是具有顶点集V(G)和边集E(G)的简单连通有限图。局部边缘反魔术着色是局部反魔术标记和边缘着色的结合。映射f∶V (G)→{1,2,…, |V (G)|}称为局部边的反魔法着色,如果每两条入射边e_1和e_2,则e_1和e_2的边权可以不相同,w(e_1)≠w(e_2),其中e = uv∈G, w(e) = f(u)+ f(V),规则是边e根据它们的权值w_e着色。局部边反幻着色已发展为局部(a,d)-反幻着色。如果边权集合形成以a为初值、d为差值的等差数列,则称为局部(a,d)-反幻着色。本研究使用的图形是向日葵图和伞形图。本研究也将讨论局部边缘(a,d)-抗魔着色的应用之一,即Sidoarjo线蜡染图案的设计。结果表明,χ_le (3,1) (Sf_n) = 3 n和χ_le (3 n / 2, 1) (U_ (m, n)) = m + 1。局部(a,d)-抗魔着色形成具有Sidoarjo地区特色的蜡染图案。
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Local edge (a, d) –antimagic coloring on sunflower, umbrella graph and its application
Suppose a graph G = (V, E) is a simple, connected and finite graph with vertex set V(G) and an edge set E(G). The local edge antimagic coloring is a combination of local antimagic labelling and edge coloring. A mapping f∶ V (G)→ {1, 2, ..., |V (G)|} is called local edge antimagic coloring if every two incident edges e_1and e_2, then the edge weights of e_1and e_2 maynot be the same, w(e_1) ≠ w(e_2), with e = uv ∈ G, w(e) = f(u)+ f(v) with the rule that the edges e are colored according to their weights, w_e. Local edge antimagic coloring has developed into local (a,d)-antimagic coloring. Local antimagic coloring is called local (a,d)-antimagic coloring if the set of edge weights forms an arithmetic sequence with a as an initial value and d as a difference value. The graphs used in this study are sunflower graphs and umbrella graphs. This research will also discuss one of the applications of local edge (a,d)-antimagic coloring, namely the design of the Sidoarjo line batik motif. The result show that χ_le(3,1) (Sf_n) = 3n and χ_le(3n/2,1) (U_(m,n) ) = m+1 . The local (a,d)-antimagic coloring is formed into a batik motif design with characteristics from the Sidoarjo region.
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