Asmiati, Asmiati and Yulianti, Lyra and Widyastuti, C.Ike (2018) Further results on locating chromatic number for amalgamation of stars linking by one path. Indonesian Journal of Combinatorics, 2 (1). pp. 50-56. ISSN 2541-2205

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Abstract

Let G = (V, E) be a connected graph. Let c be a proper coloring using k colors, namely 1, 2, · · · , k. Let Π = {S1, S2, · · · , Sk} be a partition of V (G) induced by c and let Si be the color class that receives the color i. The color code, cΠ(v) = (d(v, S1), d(v, S2), · · · , d(v, Sk)), where d(v, Si) = min{d(v, x)|x ∈ Si} for i ∈ [1, k]. If all vertices in V (G) have different color codes, then c is called as the locating-chromatic k-coloring of G. Minimum k such that G has the locating-chromatic k-coloring is called the locating-chromatic number, denoted by χL(G). In this paper, we discuss the locating-chromatic number for n certain amalgamation of stars linking a path, denoted by nSk,m, for n ≥ 1, m ≥ 2, k ≥ 3, and k > m.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Fakultas Matematika dan Ilmu Pengetahuan Alam (FMIPA) > Prodi Matematika
Depositing User: ASMIATI
Date Deposited: 26 Jun 2018 07:17
Last Modified: 26 Jun 2018 07:17
URI: http://repository.lppm.unila.ac.id/id/eprint/7825

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