  In this paper we continue the study of prime graphs of finite solvable
groups. The prime graph, or Gruenberg-Kegel graph, of a finite group G has
vertices consisting of the prime divisors of the order of G and an edge from
primes p to q if and only if G contains an element of order pq. Since the
discovery of a simple, purely graph theoretical characterization of the prime
graphs of solvable groups in 2015 these graphs have been studied in more detail
from a graph theoretic angle. In this paper we explore several new aspects of
these graphs. We characterize regular reseminant graphs and study the
automorphisms of reseminant graphs for arbitrary base graphs. We then study
minimal prime graphs on larger vertex sets by a novel regular graph
construction for base graphs and by proving results on prime graph properties
under graph products. Lastly, we present the first new way, different from
vertex duplication, to obtain a new minimal prime graph from a given minimal
prime graph.
