A polynomial algorithm determining cyclic vertex connectivity of k-regular graphs with fixed k
Abstract: For a connected graph G, a set S of vertices is a cyclic vertex cutset if \(G - S\) is not connected and at least two components of \(G-S\) contain a cycle respectively. The cyclic vertex connectivity \(c \kappa (G)\) is the cardinality of a minimum cyclic vertex cutset. In this paper, for a k-regular graph G with fixed k value, we give a polynomial time algorithm to determine \(c \kappa (G)\) and its time complexity is bounded by \(O(v^{15/2})\).
Loading