Planar Graph

Question 1
In an undirected connected planar graph G, there are eight vertices and five faces. The number of edges in G is _________.
A
15
B
13
C
11
D
10
GATE CSE 2021 SET-1   Discrete Mathematics
Question 2
Let \delta denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices with \delta \geq 3, which one of the following is TRUE?
A
In any planar embedding, the number of faces is at least \frac{n}{2}+2
B
In any planar embedding, the number of faces is less than \frac{n}{2}+2
C
There is a planar embedding in which the number of faces is less than \frac{n}{2}+2
D
There is a planar embedding in which the number of faces is at most \frac{n}{\delta +1}
GATE CSE 2014 SET-3   Discrete Mathematics
Question 3
Let G be a simple undirected planar graph on 10 vertices with 15 edges. If G is a connected graph, then the number of bounded faces in any embedding of G on the plane is equal to
A
3
B
4
C
5
D
6
GATE CSE 2012   Discrete Mathematics
Question 4
K4 and Q3 are graphs with the following structures
Which one of the following statements is TRUE in relation to these graphs?
A
K4 is planar while Q3 is not
B
Both K4 and Q3 are planar
C
Q3 is planar while K4 is not
D
Neither K4 not Q3 is planar
GATE CSE 2011   Discrete Mathematics
Question 5
Which of the following statements is true for every planar graph on n vertices?
A
The graph is connected
B
The graph is Eulerian
C
The graph has a vertex-cover of size at most 3n/4
D
The graph has an independent set of size at least n/3
GATE CSE 2008   Discrete Mathematics
Question 6
Let G be the non-planar graph with the minimum possible number of edges. Then G has
A
9 edges and 5 vertices
B
9 edges and 6 vertices
C
10 edges and 5 vertices
D
10 edges and 6 vertices
GATE CSE 2007   Discrete Mathematics
Question 7
Which one of the following graphs is NOT planar?
A
G1
B
G2
C
G3
D
G4
GATE CSE 2005   Discrete Mathematics
Question 8
Let G be a simple connected planar graph with 13 vertices and 19 edges. Then, the number of faces in the planar embedding of the graph is:
A
6
B
8
C
9
D
13
GATE CSE 2005   Discrete Mathematics
Question 9
Choose the correct alternatives ( more than one may be correct) and write the corresponding letters only:
A non-planar graph with minimum number of vertices has
A
9 edges, 6 vertices
B
6 edges, 4 vertices
C
10 edges, 5 vertices
D
9 edges, 5 vertices
GATE CSE 1992   Discrete Mathematics
There are 9 questions to complete.

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