On locating-chromatic number of complete n-ary tree

Des Welyyanti, JURUSAN MATEMATIKA FMIPA UNAND (2013) On locating-chromatic number of complete n-ary tree. AKCE International Journal of Graphs and Combinatorics. pp. 309-315. ISSN 0972-8600

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Abstract

Abstract Let c be a vertex k -coloring on a connected graph G(V, E) . Let Π = {C1, C2, ..., Ck} be the partition of V (G) induced by the coloring c . The color code cΠ(v) of a vertex v in G is (d(v, C1), d(v, C2), ..., d(v, Ck)), where d(v, Ci) = min{d(v, x)|x ∈ Ci} for 1 ≤ i ≤ k. If any two distinct vertices u, v in G satisfy that cΠ(u) = cΠ(v), then c is called a locating k-coloring of G . The locating-chromatic number of G, denoted by χL(G), is the smallest k such that G admits a locating k -coloring. Let T(n, k) be a complete n -ary tree, namely a rooted tree with depth k in which each vertex has n children except for its leaves. In this paper, we study the locating-chromatic number of T(n, k)

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