Bilangan Kromatik Lokasi Graf Helm Hm Untuk 10 ≤ m ≤ 28

Dasa, Sutanto (2023) Bilangan Kromatik Lokasi Graf Helm Hm Untuk 10 ≤ m ≤ 28. Diploma thesis, Universitas Andalas.

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Abstract

ABSTRACK Let G = (V, E) is a connected graph and c is a k-coloring of G. The color class of G is the set of colored vertexs i, denoted by Ci for 1 ≤ i ≤ k. Let Π is a ordered partition from V (G) to independent color classes that is C1, C2, ..., Ck, with vertexs of Ci given color by i, 1 ≤ i ≤ k. Distance of a vertex v ∈ V to Ci denoted by d(v, Ci) is min{d(v, x)|x ∈ Ci}. The color codes of a vertex v ∈ V is the ordered k−tuple cΠ(v) = (d(v, C1), d(v, C2), ..., d(v, Ck)) where d(v, Ci) = min{d(v, x : x ∈ Ci)} untuk 1 ≤ i ≤ k. If distinct vertices have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number χL(G) is the minimum number of colors in a locating-coloring of G. In this paper will discuss locating-chromatic number helm graph Hm for 10 ≤ m ≤ 28. helm graph with 3 ≤ i ≤ m construct with add vertex yi for 1 ≤ i ≤ m, which neighboors with vertex xi for 1 ≤ i ≤ m at wheel graph Wm. Keywords : Locating-chromatic number, Connected Graph, Wheel Graph, Helm Graph

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