Exercise · ZW-GRAPH-006 · ★★☆ Intermediate
How many edges are missing from a simple graph with \(6\) vertices and \(9\) edges to have all possible ones?
Choose one option.
Show answer
- A. 6
Explanation
There is room for \(6\cdot5/2=15\) edges in total, and \(15-9=6\).
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-002 A graph has V=\1,2,3,4\ and edges 12,\ 23,\ 34,\ 41,\ 13. How many pairs of distinct vertices are n…
- 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-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?