Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A tree has $2n$ vertices of degree $1$, $3n$ vertices of degree $2$, $n$ vertices of degree $3$. Determine the number of vertices and edges in tree.
Solution
Total number of vertices:
$V=2n+3n+n=6n$
For a tree,
$E=V-1=6n-1$
Sum of degrees:
$2n(1)+3n(2)+n(3)$
$=2n+6n+3n=11n$
By handshaking theorem,
$2E=\text{sum of degrees}$
$2(6n-1)=11n$
$12n-2=11n$
$n=2$
So,
$V=6n=6(2)=12$
$E=V-1=12-1=11$
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
