Trees with Certain Locating-chromatic Number
Journal Title: Journal of Mathematical and Fundamental Sciences - Year 2016, Vol 48, Issue 1
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 locating-chromatic 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 - t, for any integers n and t, where n > t+3 and 2 ≤ t < n/2.
Authors and Affiliations
Dian Kastika Syofyan, Edy Tri Baskoro, Hilda Assiyatun
Keywords
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- EP ID EP203102
- DOI 10.5614/j.math.fund.sci.2016.48.1.4
- Views 145
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