Indonesian Journal of Combinatorics
Vol 4, No 2 (2020)

Locating-chromatic number of the edge-amalgamation of trees

Hilda Assiyatun (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Dian Kastika Syofyan (Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung)
Edy Tri Baskoro (Unknown)



Article Info

Publish Date
31 Dec 2020

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.

Copyrights © 2020






Journal Info

Abbrev

ijc

Publisher

Subject

Computer Science & IT Decision Sciences, Operations Research & Management

Description

Indonesian Journal of Combinatorics (IJC) publishes current research articles in any area of combinatorics and graph theory such as graph labelings, optimal network problems, metric dimension, graph coloring, rainbow connection and other related topics. IJC is published by the Indonesian ...