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In his book "Large networks and graph limits", Lovász describes a multiplication operation (he calls it concatenation) on "bi-labeled graphs". An $(m,n)$ bi-labeled graph is a ...

Let $H$ be a graph and let $G=H \vee K_{1}$ be obtained by creating a new vertex and joining it to every vertex in $H$. This situation has many different names: $G$ is called the cone or the ...