Let $$G=(V,E,\gamma)$$ be an undirected graph. A vertex $$v\in V$$ and an edge $$e\in E$$ are called incident if $$v\in\gamma(e)$$.

Two different edges $$e,e'\in E$$ are called adjacent, if there is at least one vertex incident with these edges, formally $$e\neq e'$$ and $$\exists v:~ v\in \gamma(e) \cap \gamma(e')$$.

Two different vertices $$v,v'\in V$$ are neighbours or are called adjacent, if there is at at least one edge incident with these vertices, formally $$v\neq v'$$ and $$\exists e:~v,v'\in \gamma(e)$$.

Let $$v\in V$$ be a vertex of $$G$$. (Note: In the following definitions, the index $$D$$ can be omitted in the notation, if it is clear from the context, which digraph $$G$$ is concerned).

The set $$\delta_G(v):=\{e\in E: v\in \gamma(e)\}$$ is called edges incident to v.

The set $$N_G(v):=\{x\in V: x\in \delta_G(v)\}$$ is called neighbors of v.

### Example:

The values of the degrees of vertices in the above graph are:

Vertex $$v$$ Neighbours $$N(v)$$
$$a$$ $$\{b,c,d\}$$
$$b$$ $$\{a,c\}$$
$$c$$ $$\{a,b\}$$
$$d$$ $$\{a,e\}$$
$$e$$ $$\{d,e\}$$
$$f$$ $$\emptyset$$

Definitions: 1 2 3 4

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