Let G = V G , E G be a connected graph and c : V G ⟶ 1,2 , ... , k be a proper k -coloring of G . Let Π be a partition of vertices of G induced by the coloring c . We define the color code c Π v of a vertex v ∈ V G as an ordered k -tuple that contains the distance between each partition to the vertex v . If distinct vertices have distinct color code, then c is called a locating k -coloring of G . The locating chromatic number of G is the smallest k such that G has a locating k -coloring. In

more »

... paper, we determine the locating chromatic number of book graph.