  In finite group theory, studying the prime graph of a group has been an
important topic for almost the past half-century. Recently, prime graphs of
solvable groups have been characterized in graph theoretical terms only. This
now allows the study of these graphs without any knowledge of the group
theoretical background. In this paper we study prime graphs from a linear
algebra angle and focus on the class of minimally connected prime graphs
introduced in earlier work on the subject. As our main results, we determine
the determinants of the adjacency matrices and the spectra of some important
families of these graphs.
