  For any two non-negative integers h and k, h > k, an L(h, k)-colouring of a
graph G is a colouring of vertices such that adjacent vertices admit colours
that at least differ by h and vertices that are two distances apart admit
colours that at least differ by k. The smallest positive integer {\delta} such
that G permits an L(h, k)-colouring with maximum colour {\delta} is known as
the L(h, k)-chromatic number (L(h, k)-colouring number) denoted by
{\lambda}_{h,k}(G). In this paper, we discuss some interesting invariants in
hypergraphs. In fact, we study the relation between the spectral gap and L(2,
1)-chromatic number of hypergraphs. We derive some inequalities which relates
L(2, 1)-chromatic number of a k-regular simple graph to its spectral gap and
expansion constant. The upper bound of L(h, k)-chromatic number in terms of
various hypergraph invariants such as strong chromatic number, strong
independent number and maximum degree is obtained. We determine the sharp upper
bound for L(2, 1)-chromatic number of hypertrees in terms of its maximum
degree. Finally, we conclude this paper with a discussion on L(2, 1)-colouring
in cartesian product of some classes of hypergraphs.
