3. Nonexistence of constant t satisfying SG(t) = TSG
In this section, we show that there is no constant t such that SG(t) = TSG.
From the definitions, we can observe the following fact.
Observation 3.1. For a realization φ of a unit disk graph G, diam(φ) ≤ diam(G) holds.
In the next lemma we elaborate a criteria to show that a graph is not an SG(c)-graph.