in Graph Theory retagged by
1,501 views
8 votes

A non-planar graph with minimum number of vertices has

  1. $9$ edges, $6$ vertices
  2. $6$ edges, $4$ vertices
  3. $10$ edges, $5$ vertices
  4. $9$ edges, $5$ vertices
in Graph Theory retagged by
1.5k views

Subscribe to GO Classes for GATE CSE 2022

3 Answers

13 votes

A non-planar graph with minimum number of vertices has 10 edges, 5 vertices i.e K5

A non-planar graph with minimum number of edges has 9 edges, 6 vertices i.e K3,3

5 votes
Answer: C

2 Comments

Please Explain!
0
k5, k3,3 which are non planner , but k5 with minimum vertex ... 5, so no of edges n(n-1)/2 = 10 edges .
2
0 votes

Answer: C

Using  Planarity criteria relation  $e \leq 3\times v -6,$

All other option satisfies this relation except option $(C)$

i.e$10 \nleqslant 3 \times 5-6$

1 comment

sir , I think it is not sufficient condition..because  for K3,3 , 9<= 3*6 - 6 but it is non-planar graph..please correct me if I m wrong.. 

1
Answer:

Related questions

Ask
Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true