We study the question of ``how robust are the known lower bounds of labeling
schemes when one increases the number of consulted labels''. Let f be a
function on pairs of vertices. An f-labeling scheme for a family of graphs
\cF labels the vertices of all graphs in \cF such that for every graph
G\in\cF and every two vertices u,v∈G, the value f(u,v) can be inferred
by merely inspecting the labels of u and v.
This paper introduces a natural generalization: the notion of f-labeling
schemes with queries, in which the value f(u,v) can be inferred by inspecting
not only the labels of u and v but possibly the labels of some additional
vertices. We show that inspecting the label of a single additional vertex (one
{\em query}) enables us to reduce the label size of many labeling schemes
significantly