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Subjects · Leaving Cert Applied Maths

Leaving Cert Applied Maths: Graphs & network terminology

How often Graphs & network terminology comes up on the Applied Maths papers, every year it was asked, and questions to try.

HL Asked on 1 of the last 3 Higher Level papers, most recently in 2023.

OL Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Graphs & network terminology, Higher Level(6 marks)

Quick ones on Graphs & network terminology.

(a)In a network, what is a cycle?
  1. A path that visits every vertex exactly once
  2. A closed path that ends at its start vertex
  3. A single edge joining a vertex to itself
(b)What is the degree of a vertex?
  1. The number of paths passing through it
  2. The total weight of the edges at it
  3. The number of edges meeting at it
(c)In a network, what is a path?
  1. A walk in which no vertex is repeated
  2. A walk that uses every edge exactly once
  3. A walk that ends where it started
Show the answers

(a) A closed path that ends at its start vertex

(b) The number of edges meeting at it

(c) A walk in which no vertex is repeated

Your turn: Higher Level questions on Graphs & network terminology.

Higher Level

Asked on 1 of the last 3 Higher Level papers, most recently in 2023.

Every paper, year by year

YearWhere it came up
2025Not asked
2024Not asked
2023Q1

Links open the State Examinations Commission’s paper for that year.

More Graphs & network terminology questions

Graphs & network terminology, 2 marks

What is a connected graph?

  1. One where every vertex is joined directly to every other
  2. One that contains no cycles
  3. One with a path between every pair of vertices
Show the answer

One with a path between every pair of vertices

Connected means you can get from any vertex to any other, possibly through others. Every pair joined directly is a complete graph; no cycles describes a tree or forest.

Graphs & network terminology, 2 marks

What is a simple graph?

  1. One where every vertex has degree 2
  2. One with no loops and no multiple edges
  3. One with no cycles
Show the answer

One with no loops and no multiple edges

Simple means at most one edge between any two vertices and no edge from a vertex to itself. Its adjacency matrix has only 0s and 1s, with 0s on the diagonal.

Ordinary Level

Asked on 3 of the last 3 Ordinary Level papers, most recently in 2025. banker

Every paper, year by year

YearWhere it came up
2025Q4
2024Q6
2023Q4

Links open the State Examinations Commission’s paper for that year.

More Graphs & network terminology questions

Graphs & network terminology, 2 marks

What is a cycle in a graph?

  1. A path that visits every vertex and stops
  2. A single edge with a weight
  3. A path that starts and ends at the same vertex
Show the answer

A path that starts and ends at the same vertex

A cycle is a closed path: it returns to where it began without repeating any other vertex, e.g. A to B to C and back to A.

Graphs & network terminology, 2 marks

What is a weighted graph?

  1. Every edge has an arrow, e.g. a one-way street
  2. Each edge carries a number, e.g. a distance
  3. Every vertex has the same degree, e.g. 3
Show the answer

Each edge carries a number, e.g. a distance

The weight on an edge can be a distance, time or cost. Algorithms like Prim, Kruskal and Dijkstra use these weights.

Graphs & network terminology, 3 marks

How does a network differ from a scale map?

  1. It shows only connections, not true positions
  2. It shows every bend and junction in each road
  3. It must be drawn to an exact scale
Show the answer

It shows only connections, not true positions

A network keeps only which places are joined and the weights on the joins. Positions and shapes on the page do not matter, unlike on a map.

Other Applied Maths topics

All of Leaving Cert Applied Maths