How can I solve this problem

I used prover9 program to solve this problem but the program stucked at some number and never polt the result ,so I think to use Matlab .

Actually, I did not Know which function should I use ? I used For but I did not right result .

this is the problem

if you have 5 nodes (vertics ) and connect them to each other ,so every node has 4 pairs . I want to color the pairs (edges) by 3 different color {red,blue,green, } such that NO three connected edges that has the same color . I mean [ I do not want a triangle, which all its edges color by red, is going to appear] .

I start by this code

Complete (g , 5) ;

Lable(g, v, 1,2,.....5);

%% if tringle is {green , blue, red} exist (" trigle'') , if tringle { red , red , green } exist it .....etc . ( i am stuck in this command how can rewrite ?)

[Walter Roberson]

MATLAB does not provide a routine to create complete graphs except techniques such as

graph(ones(5))