Generalized L(p,q)-labellings of graphs

We deal with L(p,q)-labellings of graphs and L(p,q,r)-labellings of
graphs. By appropriate labellings we mean an assignment of non-negative
integers to vertices of graph G according to the following rules:
adjacent vertices are labelled by values differing by at least p,
vertices at distance two apart labelled by values differing by at least
q and, eventually, vertices at distance three are labelled by values
differing by at least r, where p,q,r are non-negative integers. Already
known results for L(p,q)-labelling of graphs with respect to p=0 and
q=1, p=q=1, the most common in practice p=2 and q=1, but also for p a q
in general are summarized in the first part of this talk. We then
discuss our own research, which concentrates on L(3,2,1)-labelling of
circulant graphs.