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) -> R-k such that for any two distinct vertices u and v, one has f(u).f(v) >= 1 if and only if uv is an element of E(G). The minimum value k such that G is a k-dot product graph, is called the dot product dimension rho(G) of G. These concepts were introduced for the first time by Fiduccia, Scheinerman, Trenk and Zito. In this paper, we determine the dot product dimension of unicyclic graphs. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.