For a connected graph, a minimum vertex separator is a minimum set of vertices whose removal creates at least two connected components. The vertex connectivity of the graph refers to the size of the minimum vertex separator and a graph is k-vertex connected if its vertex connectivity is k, k ≥ 1. Given a k-vertex connected graph G, the combinatorial problem… (More)
A vertex separator of a connected graph G is a set of vertices removing which will result in two or more connected components and a minimum vertex separator is a set which contains the minimum number of such vertices, i.e., the cardinality of this set is least among all possible vertex separator sets. The cardinality of the minimum vertex separator refers… (More)
Strictly Chordality-k graphs (SC k graphs) are graphs which are either cycle free or every induced cycle is exactly k, for some fixed k, k ≥ 3. Note that k = 3 and k = 4 are precisely the Chordal graphs and Chordal Bipartite graphs, respectively. In this paper, we initiate a structural and an algo-rithmic study of SC k , k ≥ 5 graphs.