Abstract: Let f be a proper edge coloring of G using k colors. For each x∈V(G), the set of the colors appearing on the edges incident with x is denoted by Sf(x) or simply S(x) if no confusion arise. If S(u)■S(v) and S(v)■S(u) for any two adjacent vertices u and v, then f is called a Smarandachely adjacent vertex distinguishing proper edge coloring using k colors, or k-SA-edge coloring. The minimum number k for which G has a Smarandachely adjacent-vertex-distinguishing proper edge coloring using k colors is called the Smarandachely adjacent-vertex-distinguishing proper edge chromatic number, or SAedge chromatic number for short, and denoted by χ’_sa(G). In this paper, we have discussed the SA-edge chromatic number of K₄∨K_n. 

Key words: complete graphs, join of graphs, Smarandachely adjacent-vertex-distinguishing proper edge coloring, Smarandachely adjacent-vertex-distinguishing proper edge chromatic number