An Algorithm For C-Vertex-Ranking Of Starlike Graphs

A c-vertex-ranking of a graph G, for a positive integer c, is a labeling of the vertices of G with integers such that, for any label i, deletion of all vertices with labels > i leaves connected components, each having at most c vertices with label i.. The c-vertex-ranking problem is to find a c-vertex ranking of a graph using least number of ranks. In this paper, for any. positive integer c, we present a linear-time algorithm for solving the c-vertex-ranking problem on a starlike graph with small central clique.