1 research outputs found
Extremal Problems Related to the Cardinality Redundance of Graphs
A dominating set of a graph is a set of vertices such that for all , either or for some . The
cardinality redundance of a vertex set , , is the number of vertices
in such that . The cardinality redundance of
is the minimum of taken over all dominating sets . A set that
achieves is a -set, and the size of the minimum
-set is . We give the maximum number of edges in a
graph with a given number of vertices and given cardinality redundance. In the
cases that , , or , we give the minimum and maximum number of
edges of graphs where is fixed. We give the minimum and
maximum values of when the number of edges are fixed and
, and we give the maximum values of when the number
of edges are fixed and .Comment: Supported by DMS-156001