1 research outputs found
Computing the metric dimension by decomposing graphs into extended biconnected components
A vertex set of an undirected graph is a
for , if for every two distinct vertices there is a vertex such that the distances between and and
the distance between and are different. The
of is the size of a smallest resolving set for . Deciding whether a
given graph has Metric Dimension at most for some integer is
well-known to be NP-complete. Many research has been done to understand the
complexity of this problem on restricted graph classes. In this paper, we
decompose a graph into its so called
and present an efficient algorithm for computing the metric dimension for a
class of graphs having a minimum resolving set with a bounded number of
vertices in every extended biconnected component. Further we show that the
decision problem METRIC DIMENSION remains NP-complete when the above limitation
is extended to usual biconnected components