  In this paper, we introduce a bisected vertex leveling of a plane graph.
Using this planar embedding, we present elementary proofs of the well-known
upper bounds in terms of the minimal crossing number on braid index $b(L)$ and
arc index $\alpha(L)$ for any knot or non-split link $L$, which are $b(L) \leq
\frac{1}{2} c(L) + 1$ and $\alpha(L) \leq c(L) + 2$. We also find a quadratic
upper bound of the minimal crossing number of delta diagrams of $L$.
