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All Journal Indonesian Journal of Combinatorics
Hilda Assiyatun
Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung
Computer Science & IT Decision Sciences, Operations Research & Management

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Locating-chromatic number of the edge-amalgamation of trees Hilda Assiyatun; Dian Kastika Syofyan; Edy Tri Baskoro
Indonesian Journal of Combinatorics Vol 4, No 2 (2020)
Publisher : Indonesian Combinatorial Society (InaCombS)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/ijc.2020.4.2.6

Abstract

The investigation on the locating-chromatic number for graphs was initially studied by Chartrand et al. on 2002. This concept is in fact a special case of the partition dimension for graphs. Even though this topic has received much attention, the current progress is still far from satisfaction. We can define the locating-chromatic number of a graph G as the smallest integer k such that there exists a proper k-coloring on the vertex-set of G such that all vertices have distinct coordinates (color codes) with respect to this coloring. Not like the metric dimension of any tree which is completely solved, the locating-chromatic number for most types of trees are still open. In this paper, we study the locating-chromatic number of trees. In particular, we give lower and upper bounds of the locating-chromatic number of trees formed by an edge-amalgamation of the collection of smaller trees. We also show that the bounds are tight.
Co-Authors Dian Kastika Syofyan Edy Tri Baskoro