Question

Supposed tree 'T' has 10 vertices of degree 4, 20 vertices of degree 3 and 30 vertices of degree 2. If all of the rest of vertices are of degree 1, then the number of verties 'T' have is ___________

• A. 102

Answer 1

The correct option is A 102
Consider number of vertices of degree $1=x$
$Totalnumberofedges=\frac{10\times 4+20\times 3+30\times 2+x\times 1}{2}$
$\frac{(x+40+60+60)}{2}=\frac{x}{2}+\frac{160}{2}$
$\frac{X}{2}+80$
$Totalnumberofvertices=10+20+3+x$
$=x+60$
Since is tree, so number of edges must be =(Number of vertices) -1
$=(x+60)-1=x+59$
Thus,
$x+59=\frac{x}{2}+80$
$2(x+59-80)=x$
$2x-2\times 21=x$
$x=42$

Total number of vertices = $x+60$
= 42 + 60 = 102