Modular Representations of Graphs
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 of G, rep(G), is the smallest integer such that G has a representation modulo r. In this paper we study the representation numbers of various graphs, such as the complete ternary tree and Harary graphs. We also give a sharp upper bound for the representation number of a connected graph G.
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تاریخ انتشار 2011