Overview (Leaving Cert Applied Maths): Quizzes

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What are the two basic components that make up any graph?

Nodes and edges

What does the degree (or valency) of a vertex represent?

How many edges meet at that node

According to the hand-shaking lemma, what does the sum of all degrees equal?

Twice the number of edges

What is a walk of length nn in a graph?

Moving along nn edges, can revisit nodes

What distinguishes a path from a walk?

All nodes visited are different

What is a cycle in graph theory?

A path that starts and ends at same vertex

In an adjacency matrix, what does a '1' in position (i,j)(i,j) indicate?

An edge from node ii to node jj

If MM is an adjacency matrix, what does MnM^n represent?

Number of walks of length nn

What defines a tree in graph theory?

Connected graph with no cycles

How many edges does a tree have if it contains nn vertices?

n−1n-1 edges

What is the first step in Prim's algorithm?

Start at any node in the graph

How do Prim's and Kruskal's algorithms differ?

Prim's builds locally, Kruskal's globally

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