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Annihilating-Ideal Graphs and Orthogonality Graphs over $\mathbb{F}_2$
We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ ω(\AG(R_4))=5<6=χ(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect,
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