  The intersection graph of a collection of trapezoids with corner points lying
on two parallel lines is called a trapezoid graph. These graphs and their
generalizations were applied in various fields, including modeling channel
routing problems in VLSI design and identifying the optimal chain of
non-overlapping fragments in bioinformatics. Using modified binary indexed tree
data structure, we design an algorithm for calculating the vertex connectivity
of trapezoid graph $G$ with time complexity $O (n \log n)$, where $n$ is the
number of trapezoids. Furthermore, we establish sufficient and necessary
condition for a trapezoid graph $G$ to be bipartite and characterize trees that
can be represented as trapezoid graphs.
