REPRESENTATION NUMBERS OF STARS Reza
نویسندگان
چکیده
A graph G has a representation modulo r if there exists an injective map f : V (G) → {0, 1, . . . , r − 1} such that vertices u and v are adjacent if and only if f(u) − f(v) is relatively prime to r. The representation number rep(G) is the smallest positive integer r for which G has a representation modulo r. In this paper we study representation numbers of the stars K1,n. We will show that the problem of determining rep(K1,n) is equivalent to determining the smallest even k for which φ(k) ≥ n: we will solve this problem for “small” n and determine the possible forms of rep(K1,n) for sufficiently large n.
منابع مشابه
Representation Numbers of Stars
A graph G has a representation modulo r if there exists an injective map f : V (G) → {0, 1, . . . , r−1} such that vertices u and v are adjacent if and only if f(u)−f(v) is relatively prime to r. The representation number rep(G) is the smallest positive integer r for which G has a representation modulo r. In this paper we study representation numbers of the stars K1,n. We will show that the pro...
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