  The structure of the character degree graphs $\Delta(G)$, i.e. the prime
graphs on the set $\mathrm{cd}(G)$ of the irreducible character degrees of a
finite group $G$, such that $G$ is solvable and $\Delta(G)$ has diameter three,
remains an intriguing area of study. However, a comprehensive understanding of
these structures remains elusive. In this paper, we prove some properties and
provide an infinite series of examples of this class of graphs, building on the
ideas of Mark Lewis.
