  One of the most famous applications of Graph Theory is in the field of
Channel Assignment Problems. There are varieties of graph colouring concepts
that are used for different requirements of frequency assignments in
communication channels. We introduce here L(t, 1)-colouring of graphs. This has
its foundation in T-colouring and L(p, q)-colouring. For a given finite set T
including zero, an L(t, 1)-colouring of a graph G is an assignment of
non-negative integers to the vertices of G such that the difference between the
colours of adjacent vertices must not belong to the set T and the colours of
vertices that are at distance two must be distinct. The variable t in L(t, 1)
denotes the elements of the set T. For a graph G, the L(t, 1)-span of G is the
minimum of the highest colour used to colour the vertices of a graph out of all
the possible L(t, 1)-colourings. It is denoted by $\lambda_{t,1} (G)$. We study
some properties of L(t, 1)-colouring. We also find upper bounds of
$\lambda_{t,1} (G)$ of selected simple connected graphs.
