26 research outputs found
On the Roman Bondage Number of Graphs on surfaces
A Roman dominating function on a graph is a labeling such that every vertex with label has a neighbor
with label . The Roman domination number, , of is the
minimum of over such functions. The Roman bondage
number is the cardinality of a smallest set of edges whose removal
from results in a graph with Roman domination number not equal to
. In this paper we obtain upper bounds on in terms of
(a) the average degree and maximum degree, and (b) Euler characteristic, girth
and maximum degree. We also show that the Roman bondage number of every graph
which admits a -cell embedding on a surface with non negative Euler
characteristic does not exceed .Comment: 5 page
Upper bounds for domination related parameters in graphs on surfaces
AbstractIn this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorientable genus and maximum degree
On equality in an upper bound for the acyclic domination number
A subset of vertices in a graph is acyclic if the subgraph it induces contains no cycles. The acyclic domination number of a graph is the minimum cardinality of an acyclic dominating set of . For any graph with vertices and maximum degree , . In this paper we characterize the connected graphs and the connected triangle-free graphs which achieve this upper bound