This thesis is divided into two parts. In the first part, the concept of nowhere-zero flows has been introduced. A graph has a nowhere-zero k-flow if its edges can be oriented and assigned numbers ±1, …, ±(k-1) so that for every vertex, the sum of the values on incoming edges equals the sum on the outgoing ones. This concept was introduced by Tutte in 1954. After that Jaeger et al. introduced the concept of group connectivity as an extension of nowhere-zero flows. In this part we consider the most important results on nowhere-zero flows, then we study the concept of group connectivity. In the second part, we study the graphs with three distinct eigenvalues. The problem of graphs with few distinct eigenvalues was first raised by Doob. In this part we review the results on graphs with three distinct eigenvalues, also we present a characterization of these graphs in a special case.
