2 research outputs found
On the Roman bondage number of a graph
A Roman dominating function on a graph is a function
such that every vertex with has at
least one neighbor with . The weight of a Roman dominating
function is the value . The minimum weight of a
Roman dominating function on a graph is called the Roman domination number,
denoted by . The Roman bondage number of a graph
with maximum degree at least two is the minimum cardinality of all sets
for which . In this paper, we
first show that the decision problem for determining is NP-hard
even for bipartite graphs and then we establish some sharp bounds for and characterizes all graphs attaining some of these bounds.Comment: 15 pages, 35 reference
On Bondage Numbers of Graphs -- a survey with some comments
The bondage number of a nonempty graph is the cardinality of a smallest
edge set whose removal from results in a graph with domination number
greater than the domination number of . This lecture gives a survey on the
bondage number, including the known results, problems and conjectures. We also
summarize other types of bondage numbers.Comment: 80 page; 14 figures; 120 reference