| Abstrakt: |
Given a graph G = (V , E) , a vertex u ∈ V ve-dominates all edges incident to any vertex of N G [ u ] . A set S ⊆ V is a ve-dominating set if for all edges e ∈ E , there exists a vertex u ∈ S such that u ve-dominates e. Lewis (Vertex-edge and edge-vertex parameters in graphs. Ph.D. thesis, Clemson, SC, USA, 2007) proposed a linear time algorithm for ve-domination problem for trees. In this paper, we have constructed an example where the algorithm proposed by Lewis, fails. We have proposed linear time algorithms for ve-domination and independent ve-domination problem in block graphs, which is a superclass of trees. We have also proposed a linear time algorithm for weighted ve-domination problem in trees. We have also proved that finding minimum ve-dominating set is NP-complete for undirected path graphs. Finally, we have characterized the trees with equal ve-domination and independent ve-domination number. [ABSTRACT FROM AUTHOR] |
Full text from SpringerLink