Graph Theory/Nodes & edges

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Basic Definitions

Graph 

an ordered pair (V,E):

• V is the vertex set, where the elements are vertices; often written as V(G)
• E is the edge set, where the elements are edges; often written as E(G)

Lines that intersect(交叉) are (usually) ignored as irrelevant(无关紧要的) (see planarity(平面性) for where intersections do matter)

Two graphs are considered equal when V₁ = V₂ and E₁ = E₂.

Order 

the number of vertices in a graph, denoted(记作)| V(G) | , often using n

Size 

the number of edges in a graph, denoted | E(G) | , often using m

Notice: the order of any graph must be at least 1 (n≥1).

• If n = 1, the graph is considered trivial(平凡的).
• If n≥2, the graph is considered nontrivial(非平凡的).