VERTEX DISTINGUISHING PROPER EDGE COLORINGS OF THE JOIN GRAPHS - Petrosyan, Tigran K. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2025)
A proper edge coloring of a graph G is a mapping f:E(G)Z_≥ 0 such that f(e) ot=f(e’) for every pair of adjacent edges e and e’ in G. A proper edge coloring f of a graph G is called vertex distinguishing if for any different vertices u,v V(G), S(u,f) e S(v,f), where S(v,f) = {f(e) | e = wv E(G)}. The minimum number of colors required for a vertex distinguishing proper coloring of a graph G is denoted by χ’_vd(G) and called vertex distinguishing chromatic index of G. In this paper we provide lower and upper bounds on the vertex distinguishing chromatic index of the join graphs.