On the Decycling Number of Bubble-sort Star Graphs

Abstract

Bubble-sort star graphs are a combination of star graphs and bubble sort graphs. They are bipartite graphs and also form a family of Cayley graphs. The decycling number of a graph is the minimum number of vertices whose removal from the graph results in an acyclic subgraph. In this paper, we prove the decycling number D(n) of an n-dimensional bubblesort star graph for n 5. We also show D(n) satisfies the inequalities for n 6:2 − 2( n−1 2 )! + 1 otherwise.