Answer by Rócherz for Proof for a property of graph laplacian and its...
Rewrite $L(G^c)$ as $nI_n -e^T_n e_n -L(G)$, where $e_n$ is the all-ones $n$-tuple row vector, and $e^T_n e_n = J_n$. Note that $(e_n, 0)$ is still a trivial (row) eigenpair of...
View ArticleProof for a property of graph laplacian and its complement?
Here it saysLet $L(G)$ be the Laplacian of an undirected graph. $L(G)+L(G^c)=n I_n-J_n$Where $J_n$ is a matrix with all entries $1$. Then how do we prove this (page $224$; eq....
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