寻找平方补图：不存在性结果和识别的复杂性
Searching for square-complementary graphs: non-existence results and complexity of recognition
摘要：
一个图是平方补图（square-complementary，简称squco），如果它的平方和补图是同构的。证明了不存在围长为6的squco图，证明了每一个二部图都是squco二部图的诱导子图，证明了squco图的识别问题是图同构完全的，证明了不存在非平凡squco图既是二部图又是平面图.这些结果解决了离散数学327（2014）62-75中提出的三个未决问题。
英文摘要：
A graph is square-complementary (squco, for short) if its square and complement are isomorphic. We prove that there are no squco graphs with girth 6, that every bipartite graph is an induced subgraph of a squco bipartite graph, that the problem of recognizing squco graphs is graph isomorphism complete, and that no nontrivial squco graph is both bipartite and planar. These results resolve three of the open problems posed in Discrete Math. 327 (2014) 62-75.
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