A k-edge colouring (not necessarily proper) of a graph with colours in {1,2,…,k} is neighbour sum distinguishing if, for any two adjacent vertices, the sums edges incident each them are distinct. The smallest value k such that G exists denoted by χ∑e(G). When we add additional restriction must be proper, then χ∑′(G). Such colourings studied on connected at least 3 vertices. There famous conject...