# ME test series question on graph theory

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Please explain how did they get that equation in E and V.
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Consider a graph $G$ with $2^{n}$ vertices where the level of each vertex is a $n$ bit binary string represented as $a_{0},a_{1},a_{2},.............,a_{n-1}$, where each $a_{i}$ is $0$ or $1$ ... $x$ and $y$ denote the degree of a vertex $G$ and number of connected component of $G$ for $n=8.$ The value of $x+10y$ is_____________
Let $G$ be a graph on $n$ vertices with $4n-16$ edges.Consider the following: 1. There is a vertex of degree smaller than $8$ in $G.$ 2. There is a vertex such that there are less than $16$ vertices at a distance exactly $2$ from it. Which of the following is TRUE: 1 only 2 only Both 1 and 2 Neither 1 nor 2