is the line graph of the complete graph on vertices, , i.e. each edge in is represented by a vertex in , where these vertices in are adjacent if the edges in are adjacent to the same vertex.

What "advance knowledge" do you need?? Please asking this on all my posts when you don't even specify what I need to update the question with.

L(K) K L(K) L(K) Bonus Question: Let p be a prime congruent to 3 mod 4. Show that L(Kp) is a Cayley graph. Hint: Consider the group AGL(1, p) = {x H ar +bla Z, be Zp}