| $\text{Graph}$ | $\text{No. of vertices}$ |
| $\text{Line graph of Petersen graph}$ | $15$ |
| $\text{Line graph of Heawood graph}$ | $21$ |
| $\text{Line graph of Tutte's 8-cage}$ | $45$ |
| $\text{Flag graph of }PG(2,3)$ | $52$ |
| $\text{Flag graph of }PG(2,4)$ | $105$ |
| $\text{Line graph of Hoffman--Singleton graph}$ | $175$ |
| $\text{Flag graph of }PG(2,5)$ | $186$ |
| $\text{Line graph of Tutte's 12-cage}$ | $189$ |
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Graphs by family
Last updated: 31 March 2019