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All Journal Indonesian Journal of Combinatorics
A. Asmiati
University of Lampung
Computer Science & IT Decision Sciences, Operations Research & Management

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On the Locating Chromatic Number of Barbell Shadow Path Graph A. Asmiati; Maharani Damayanti; Lyra Yulianti
Indonesian Journal of Combinatorics Vol 5, No 2 (2021)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2021.5.2.4

Abstract

The locating-chromatic number was introduced by Chartrand in 2002. The locating chromatic number of a graph is a combined concept between the coloring and partition dimension of a graph. The locating chromatic number of a graph is defined as the cardinality of the minimum color classes of the graph. In this paper, we discuss about the locating-chromatic number of shadow path graph and barbell graph containing shadow graph.
Further Results on Locating Chromatic Number for Amalgamation of Stars Linking by One Path A. Asmiati; Lyra Yulianti; C. Ike Tri Widyastuti
Indonesian Journal of Combinatorics Vol 2, No 1 (2018)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (222.469 KB) | DOI: 10.19184/ijc.2018.2.1.6

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.
Co-Authors C. Ike Tri Widyastuti Maharani Damayanti Yulianti, Lyra