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In finite group theory, studying the prime graph of a group has been animportant topic for almost the past half-century. Recently, prime graphs ofsolvable groups have been characterized in graph theoretical terms only. Thisnow allows the study of these graphs without any knowledge of the grouptheoretical background. In this paper we study prime graphs from a linearalgebra angle and focus on the class of minimally connected prime graphsintroduced in earlier work on the subject. As our main results, we determinethe determinants of the adjacency matrices and the spectra of some importantfamilies of these graphs.

The Adjacency Spectra of Some Families of Minimally Connected Prime Graphs