Minimal feedback vertex sets in directed split-stars

In a graph G = (V, E), a subset F ⊂ V(G) is a feedback vertex set of G if the subgraph induced by V(G) \ F is acyclic. In this paper, we propose an algorithm for finding a small feedback vertex set of a star graph. Indeed, our algorithm can derive an ...

A distance-k dominating set D of a directed graph G is a set of vertices such that for every vertex v of G, there is a vertex u ∈ D and the distance between u and v is at most k. Minimum distance-k dominating set is especially important in communication ...

The matching preclusion number of a graph is the minimum number of edges the deletion of which results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those ...