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All Journal Limits: Journal of Mathematics and Its Applications
Putri, Azizah Riana
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Computer Science & IT Mathematics

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Bilangan Kromatik Lokasi Graf Tentakel Putri, Azizah Riana; Sy, Syafrizal; Helmi, Monika Rianti
Limits: Journal of Mathematics and Its Applications Vol. 22 No. 2 (2025): Limits: Journal of Mathematics and Its Applications Volume 22 Nomor 2 Edisi Ju
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v22i2.3462

Abstract

The locating-chromatic number of a graph was introduced by Chartrand et al. in 2002, which is a combined concept between the vertex coloring and partition dimension of a graph. The locating-chromatic number of a graph is a grouping of vertices on a graph based on color, which is called a color class, provided that each vertex on the graph has a different color code. Determining the locating-chromatic number of a graph is done by constructing the lower and upper bound of the locating-chromatic number of the graph. In this paper, we determine the locating-chromatic number of the tentacle graph, which is denoted by T_(k,m,n). Tentacle Graph is a graph constructed from a triangular book graph Bt_n whose common edge is amalgamated with C_k. Then two vertices in C_k that are adjacent to the vertex associated with the terminal edge are amalgamated with the star graphs S_(n_1) and S_(n_2). By determining the lower and upper bounds of the location chromatic number, it is obtained that the location chromatic number of Tentacle Graph is 4, m=1,n=2, n+1, for m>=1, n>= m + 2, and m + 2, for m > 1, n < m + 2.
Co-Authors Helmi, Monika Rianti Syafrizal Sy, Syafrizal