Efficient identification of Web communities
Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining
On the Hardness of Approximating Minimum Monopoly Problems
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
On the Metric Dimension of Cartesian Products of Graphs
SIAM Journal on Discrete Mathematics
On the global offensive alliance number of a graph
Discrete Applied Mathematics
Partitioning a graph into offensive k-alliances
Discrete Applied Mathematics
Handbook of Product Graphs, Second Edition
Handbook of Product Graphs, Second Edition
Computing global offensive alliances in Cartesian product graphs
Discrete Applied Mathematics
| Hi-index | 0.04 |
Let G=(V,E) be a graph. For a non-empty subset of vertices S@?V, and vertex v@?V, let @d"S(v)=|{u@?S:uv@?E}| denote the cardinality of the set of neighbors of v in S, and let S@?=V-S. Consider the following condition: (1)@d"S(v)=@d"S"@?(v)+k, which states that a vertex v has at least k more neighbors in S than it has in S@?. A set S@?V that satisfies Condition (1) for every vertex v@?S is called a defensivek-alliance and for every vertex v in the open neighborhood of S is called an offensivek-alliance. A subset of vertices S@?V is a powerfulk-alliance if it is both a defensive k-alliance and an offensive (k+2)-alliance. Moreover, a subset X@?V is a defensive (an offensive or a powerful) k-alliance free set if X does not contain any defensive (offensive or powerful, respectively) k-alliance. In this article we study the relationships between defensive (offensive, powerful) k-alliance free sets in Cartesian product graphs and defensive (offensive, powerful) k-alliance free sets in the factor graphs.