  A set of lines through the origin in Euclidean space is called equiangular
when any pair of lines from the set intersects with each other at a common
angle. We study the maximum size of equiangular lines in Euclidean space and
use graph theoretic approach to prove that all the currently known construction
for maximum equiangular lines in $\mathbb R^d$ cannot add another line to form
a larger equiangular set of lines if $14 \leq d \leq 20$ and $d \neq 15$. We
give new constructions of large equiangular lines which are 248 equiangular
lines in $\mathbb R^{42}$, 200 equiangular lines in $\mathbb{R}^{41}$, 168
equiangular lines in $\mathbb{R}^{40}$, 152 equiangular lines in $\mathbb
R^{39}$ with angle $1/7$, and 56 equiangular lines in $\mathbb R^{18}$ with
angle $1/5$.
