Exercise · ZW-GRAPH-003 · ★☆☆ Basic
Which of these edge sets cannot belong to a simple graph on \(\{a,b,c\}\)?
Choose one option.
Show answer
- D. \(\{aa,bc\}\)
Explanation
The edge \(aa\) is a loop, joining a vertex to itself; a simple graph only allows pairs of distinct vertices.
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?
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- 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?