Vertex set

In graph theory, the vertex set ^[1] of a graph $G$ is the set of all its vertices. Together with the edge set, it forms the pair $G=(V,E)$ that defines the graph.

Definition

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Definition 1 (Vertex set)

Let $G=(V,E)$ be a graph. The set $V$ is called the vertex set of $G$, and its elements are the vertices of $G$.

Notation

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The vertex set of a graph $G$ is denoted $V(G)$, or simply $V$ when the graph is unambiguous

References

1. [1]

   “Graph (discrete mathematics)”, Wikipedia, Available: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics), Accessed: 2026-07-15 ↩