Dot Product Dimension of Unicyclic Graphs

A graph g = (v (g); e(g)) is called a k-dot product graph if there is a function f : v (g) −! rk suchthat for any two distinct vertices u and v, one has f(u):f(v) ≥ 1 if and only if uv 2 e(g). the minimumvalue k such that g is a k-dot product graph, is called the dot product dimension ρ(g) of g. theseconcepts for the first time were introduced by fiduccia, scheinerman, trenk and zito. in this paper, wedetermine the dot product dimension of unicyclic graphs.