论文标题
来自$ e_8 $ root System的量子同构强大的定期图
Quantum isomorphic strongly regular graphs from the $E_8$ root system
论文作者
论文摘要
在本文中，我们给出了一对量子同构，非同构强的示例，即从所有平面图中具有相同同态计数的非同态强态图。这对由$ e_8 $ root Systems跨越的$ 120 $行的正交图组成，排名$ 4 $图形，其补充是由Brouwer，Ivanov和Klin首先发现的。这两个图都是很常规的，带有参数$（120、63、30、36）$。使用GODSIL-MCKAY开关，我们获得了具有相同参数的更多量子同构，非同构的强态图。
In this article, we give a first example of a pair of quantum isomorphic, non-isomorphic strongly regular graphs, that is, non-isomorphic strongly regular graphs having the same homomorphism counts from all planar graphs. The pair consists of the orthogonality graph of the $120$ lines spanned by the $E_8$ root system and a rank $4$ graph whose complement was first discovered by Brouwer, Ivanov and Klin. Both graphs are strongly regular with parameters $(120, 63, 30, 36)$. Using Godsil-McKay switching, we obtain more quantum isomorphic, non-isomorphic strongly regular graphs with the same parameters.
