Exercise · ZW-GRAPH-002 · ★☆☆ Basic
A graph has \(V=\{1,2,3,4\}\) and edges \(12,\ 23,\ 34,\ 41,\ 13\). How many pairs of distinct vertices are not joined?
Choose one option.
Show answer
- A. 1
Explanation
There are \(6\) possible pairs and \(5\) are edges; only the pair \(24\) is missing.
Review the concept: Graph
A graph \(G\) is a set \(V\) of vertices together with a set \(E\) of edges, each formed by two distinct vertices.
\[G=(V,E),\qquad E\subseteq\{\{u,v\}:\ u,v\in V,\ u\neq v\}\]
More practice problems: graph
- ZW-GRAPH-001 What is the largest number of edges in a simple graph with 5 vertices?
- ZW-GRAPH-003 Which of these edge sets cannot belong to a simple graph on \a,b,c\?
- ZW-GRAPH-004 Which statement is true in a simple graph?
- ZW-GRAPH-005 How many different graphs can be formed on the labelled vertices \1,2,3\?
- ZW-GRAPH-006 How many edges are missing from a simple graph with 6 vertices and 9 edges to have all possible one…
- ZW-GRAPH-007 A simple graph with n vertices has 45 edges, all the possible ones. What is n?
- ZW-GRAPH-008 For which (vertices, edges) pair does a simple graph exist?
- ZW-GRAPH-009 How many simple graphs on the labelled vertices \1,2,3,4\ have exactly 5 edges?