1 research outputs found
On the generalized (edge-)connectivity of graphs
The generalized -connectivity of a graph was introduced
by Chartrand et al. in 1984. It is natural to introduce the concept of
generalized -edge-connectivity . For general , the
generalized -edge-connectivity of a complete graph is obtained. For , tight upper and lower bounds of and are given
for a connected graph of order , that is, and . Graphs of order such that
and
are characterized, respectively.
Nordhaus-Gaddum-type results for the generalized -connectivity are also
obtained. For , we study the relation between the edge-connectivity and
the generalized 3-edge-connectivity of a graph. Upper and lower bounds of
for a graph in terms of the edge-connectivity of
are obtained, that is, ,
and two graph classes are given showing that the upper and lower bounds are
tight. From these bounds, we obtain that if is a connected planar graph, and the relation between the
generalized 3-connectivity and generalized 3-edge-connectivity of a graph and
its line graph.Comment: 15 page