Representations of Split Graphs, Their Complements, Stars, and Hypercubes

A graph G has a representation modulo n if there exists an injective map f : V (G) → {0, 1, . . . , n} such that vertices u and v are adjacent if and only if |f(u) − f(v)| is relatively prime to n. The representation number rep(G) is the smallest n such that G has a representation modulo n. We present new results involving representation numbers for stars, split graphs, complements of split graphs, and hypercube