The disconnection number of a graph

Helma Gladdines, Marcel van de Vel
2011 Topology and its Applications  
The disconnection number d( X) is the least number of points in a connected topological graph X such that removal of d( X) points will disconnect X (Nadler, 1993 [6]). Let D n denote the set of all homeomorphism classes of topological graphs with disconnection number n. The main result characterizes the members of D n+1 in terms of four possible operations on members of D n . In addition, if X and Y are topological graphs and X is a subspace of Y with no endpoints, then d( X) d(Y ) and Y
more » ... from X with exactly d(Y ) − d( X) operations. Some upper and lower bounds on the size of D n are discussed. The algorithm of the main result has been implemented to construct the classes D n for n 8, to estimate the size of D 9 , and to obtain information on certain subclasses such as non-planar graphs (n 9) and regular graphs (n 10).
doi:10.1016/j.topol.2010.11.019 fatcat:znrk6g5xebak5hizd3oghw6xfu