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Arfin, Arfin
Universitas Muhammadiyah Surabaya
Religion Agriculture, Biological Sciences & Forestry Arts Humanities Decision Sciences, Operations Research & Management Education Languange, Linguistic, Communication & Media Mathematics Physics Social Sciences Other

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Journal : Journal of the Indonesian Mathematical Society

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The Locating-Chromatic Number of Some Jellyfish Graphs Arfin, Arfin
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1627

Abstract

Let c be a proper coloring of a graph G = (V, E) with k colors which induces a partition Π of V (G) into color classes L1, L2, . . . , Lk . For each vertex v in G, the color code cΠ(v) is defined as the ordered k-tuple (d(v, L1), d(v, L2), . . . , d(v, Lk )), where d(v, Li) represents the minimum distance from v to all other vertices u in Li(1 ≤ i ≤ k). If every vertex possesses unique color codes, then c is called a locating-k-coloring in G. If k is the minimum number such that c is a locating-k-coloring in G, then the locating-chromatic number of G is χL(G) = k. In this paper, the author determine the locating-chromatic number of some Jellyfish Graphs.
Co-Authors Boriboon, Gumpanat Dafid Slamet Setiana Ester Manthalina Hutabarat, Christina Eva Wulanningtyas, Melania Fauzi, Rizky Reza Fitriani Fitriani Gustia, Waode Haryanto Panjaitan, Muchtar Hermanto Hermanto Hutabarat, Christina Ester Manthalina Ishak Bagea Jamaluddin Jamaluddin Jaya Nur, Makmur La Ndibo, Yaman Lilianti, Lilianti Linling, Yudiani M. Sukarno M., Rahmawati marpaung, winida Melania Eva Wulanningtyas Mujiati Mujiati ndibo, yaman la Nurzaima, Nurzaima Purba, Benedictus Janrian Risya Pramana Situmorang Tomi, Tomi Usman Usman Xaveriano Waresindo, William