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SUTANTO, DASA
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Agriculture, Biological Sciences & Forestry Astronomy Biochemistry, Genetics & Molecular Biology Chemistry Earth & Planetary Sciences Energy Immunology & microbiology Neuroscience Physics

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On locating-chromatic number of helm graph H_m FOR 10m28 WELYYANTI, DES; SUTANTO, DASA; YULIANTI, LYRA
Jurnal Natural Volume 24 Number 3, October 2024
Publisher : Universitas Syiah Kuala

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/jn.v24i3.33190

Abstract

Let G = (V,E) be a connected graph and c be a k-coloring of G. The color class S_i of G is a set of vertices given color i, for 1 i k. Let = {S_1,S_2,,S_k} be an ordered partition of V(G). The color code of a vertex v $in$ (element) V(G) is defined as the ordered k--tuplec_ (v)=(d(v,S_1),d(v,S_2),...,d(v,S_k)),where d(v,S_i) = min{d(v,x)| x $in$ (element) S_i} for 1 i k. If distinct vertices have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number _L (G) is the minimum number of colors in a locating-coloring of G. This paper discusses the locating-chromatic number of helm graph H_m for 10 m 28. Helm graph H_m is constructed by adding some leaves to the corresponding vertices of wheels W_m, for m 3.
Co-Authors Des Welyyanti Yulianti, Lyra