On the Decycling Number of Bubble-sort Star Graphs
Yu-Zhe Liu, Shyue-Ming Tang, Jou-Ming Chang
TL;DR
This paper investigates the decycling number of bubble-sort star graphs, providing exact values for small dimensions and bounds for larger ones, contributing to understanding their structural properties.
Contribution
It determines the decycling number for n <= 5 and establishes inequalities for n >= 6, advancing knowledge of these graphs' cycle-breaking characteristics.
Findings
Decycling number D(n) for n <= 5 is explicitly calculated.
D(n) satisfies certain inequalities for n >= 6.
The study enhances understanding of bubble-sort star graphs' acyclic subgraphs.
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 bubble-sort star graph for n <= 5. We also show D(n) satisfies the inequalities for n >= 6.
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Taxonomy
TopicsInterconnection Networks and Systems · Advanced Graph Theory Research · graph theory and CDMA systems