the locating chromatic number of the join of graphs

‎let $f$ be a proper $k$-coloring of a connected graph $g$ and‎ ‎$pi=(v_1,v_2,ldots,v_k)$ be an ordered partition of $v(g)$ into‎ ‎the resulting color classes‎. ‎for a vertex $v$ of $g$‎, ‎the color‎ ‎code of $v$ with respect to $pi$ is defined to be the ordered‎ ‎$k$-tuple $c_{{}_pi}(v)=(d(v,v_1),d(v,v_2),ldots,d(v,v_k))$‎, ‎where $d(v,v_i)=min{d(v,x):~xin v_i}‎, ‎1leq ileq k$‎. ‎if‎ ‎distinct vertices have distinct color codes‎, ‎then $f$ is called a‎ ‎locating coloring‎. ‎the minimum number of colors needed in a‎ ‎locating coloring of $g$ is the locating chromatic number of $g$‎, ‎denoted by $cchi_{{}_l}(g)$‎. ‎in this paper‎, ‎we study the locating chromatic number of the join of graphs‎. ‎we show that when $g_1$ and $g_2$ are two connected graphs with diameter at most two‎, ‎then $cchi_{{}_l}(g_1vee g_2)=cchi_{{}_l}(g_1)+cchi_{{}_l}(g_2)$‎, ‎where $g_1vee g_2$ is the join of $g_1$ and $g_2$‎. ‎also‎, ‎we determine the‎ ‎locating chromatic number of the join of paths‎, ‎cycles and complete multipartite graphs‎.