ON THE LOCATING-CHROMATIC NUMBERS OF SUBDIVISIONS OF FRIENDSHIP GRAPH

Abstract

Let c be a k-coloring of a connected graph G and let π = fC1;C2; : : : ;Ckg be the partition of V (G) induced by c. For every vertex v of G, let cκ(v) be the coordinate of v relative to π, that is cπ (v) = (d(v;C1); d(v;C2); : : : ; d(v;Ck)), where d(v;Ci) = minfd(v; x)jx 2 Cig. If every two vertices of G have different coordinates relative to π, then c is said to be a locating k-coloring of G. The locating-chromatic number of G, denoted by L(G), is the least k such that there exists a locating k-coloring of G. In this paper, we determine the locating-chromatic numbers of some subdivisions of the friendship graph Frt, that is the graph obtained by joining t copies of 3-cycle with a common vertex, and we give lower bounds to the locating-chromatic numbers of few other subdivisions of Frt.