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- Title
Trees with Certain Locating-Chromatic Number.
- Authors
Syofyan, Dian Kastika; Baskoro, Edy Tri; Assiyatun, Hilda
- Abstract
The locating-chromatic number of a graph G can be defined as the cardinality of a minimum resolving partition of the vertex set V(G) such that all vertices have distinct coordinates with respect to this partition and every two adjacent vertices in G are not contained in the same partition class. In this case, the coordinate of a vertex v in G is expressed in terms of the distances of v to all partition classes. This concept is a special case of the graph partition dimension notion. Previous authors have characterized all graphs of order n with locatingchromatic number either n or n - 1. They also proved that there exists a tree of order n, n ≥ 5, having locating-chromatic number k if and only if k ∊ {3,4,..., n - 2, n}. In this paper, we characterize all trees of order n with locating-chromatic number n - n, for any integers n and t, where n > t + 3 and 2 ≤ t < n/2.
- Subjects
TREE graphs; CHROMATIC polynomial; GEOMETRIC vertices; SET theory; INTEGERS
- Publication
Journal of Mathematical & Fundamental Sciences, 2016, Vol 48, Issue 1, p39
- ISSN
2337-5760
- Publication type
Article
- DOI
10.5614/j.math.fund.sci.2016.48.1.4