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Topic 3.14Math AI HL8 flashcards

Graph theory (HL only)

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Card 1 of 83.14.1
3.14.1
Question

What are the two basic parts of a graph?

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All Flashcards in Topic 3.14

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3.14.18 cards

Card 1concept
Question

What are the two basic parts of a graph?

Answer

Vertices (the dots/points) and edges (the lines joining pairs of vertices).

Card 2concept
Question

What is the degree of a vertex?

Answer

The number of edge-ends meeting at that vertex (a loop counts as 2).

Card 3formula
Question

State the handshake lemma.

Answer

The sum of all vertex degrees equals 2 × (number of edges): Σ deg(v) = 2E.

Card 4concept
Question

Why must the number of odd-degree vertices be even?

Answer

Because the total degree Σ deg = 2E is always even, the odd degrees must pair up to keep the sum even.

Card 5formula
Question

What is a complete graph Kₙ, and how many edges does it have?

Answer

Every pair of vertices is joined; it has n(n − 1)/2 edges and every vertex has degree n − 1.

Card 6formula
Question

What is a tree, and how many edges does a tree on n vertices have?

Answer

A connected graph with no cycles; it has exactly n − 1 edges.

Card 7concept
Question

What is a bipartite graph?

Answer

The vertices split into two groups, with edges only between the groups (never within a group).

Card 8concept
Question

Distinguish a trail, a path and a cycle.

Answer

Trail = no repeated edge (may revisit a vertex); path = no repeated vertex; cycle = a path that returns to its start.

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