Threshold graphs can be characterized in many ways. One way of obtaining a threshold graph is through an iterative process that starts with an isolated vertex, and where, at each step, either a new isolated vertex is added, or a vertex adjacent to all previous vertices (dominating vertex) is added.
In this talk, we study the spectral invariant of $q(G)$ for connected threshold graphs of a fixed order $n$.
This is a joint work with Dean Crnković and Andrea Švob.
 Crnković, D., Maksimović, M., Rodrigues, B. G., Rukavina, S.: Self-orthogonal codes from the strongly regular graphs on up to 40 vertices, Adv. Math. Commun. 10 (2016), 555-582.
 Crnković, D., Rukavina, S., Švob, A.: Self-orthogonal codes from equitable partitions of association schemes, ArXiv preprint, https://arxiv.org/pdf/1903.01832.pdf