Mathematical Notation for Graph Properties

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I have a graph with two sets, vertices and edges, $G=(V,E)$. In my case every vertex and every edge have some attributes like $type$.

What is the mathematical correct way to get the value of a vertex' property? Maybe $property(v)$ where $property$ is the property name and $v$ the single vertex?

What is the correct way to get only the vertices (a set of vertices) that have a specific value? For example if I want a set of vertices that only have $1$ as the value of $type$?