. Let D be a simple graph on 10 vertices such that there is a vertex of degree 1, a vertex of degree 2, a vertex of degree 3, a vertex of degree 4, a vertex of degree 5, a vertex of degree 6, a vertex of degree 7, a vertex of degree 8 and a vertex of degree 9. What can be the degree of the last vertex?
a) 4
b) 0
c) 2
d) 5
Answers
Given : D be a simple graph on 10 vertices such that there is
a vertex of degree 1,
a vertex of degree 2,
a vertex of degree 3,
a vertex of degree 4,
a vertex of degree 5,
a vertex of degree 6,
a vertex of degree 7,
a vertex of degree 8 an
d a vertex of degree 9
To Find : What can be the degree of the last vertex
a) 4
b) 0
c) 2
d) 5
Solution:
a vertex of degree 1
a vertex of degree 2
upto
vertex of degree 9
Total Degrees = ( 1 + 2 + 3 + . + . + . + 9)
= 9(10)/2
= 45
Number of digress are twice the number of the edges in the graph.
Hence Number of digress are always even
degree of the last vertex can be 5 only
as 45 + 5 = 50 is only possible even degree
Rest all other options leads to odd numbers ( 45 + 4 = 49 , 45 + 0 = 45 , 45 + 2 = 47)
degree of the last vertex can be 5
Learn More:
A connected graph has 9 vertices having degrees 2, 2, 2, 3, 3, 3, 4, 4 ...
https://brainly.in/question/13904163
cuboid looks like a rectangular box. It has ______ faces. Each face ...
brainly.in/question/12251134
How many edges, vertices and faces does a triangular prism have ...
brainly.in/question/4616510