The Spectral Gap of Graphs Arising From Substring Reversals

Fan Chung, Josh Tobin


The substring reversal graph $R_n$ is the graph whose vertices are the permutations $S_n$, and where two permutations are adjacent if one is obtained from a substring reversal of the other. We determine the spectral gap of $R_n$, and show that its spectrum contains many integer values. Further we consider a family of graphs that generalize the prefix reversal (or pancake flipping) graph, and show that every graph in this family has adjacency spectral gap equal to one.


Spectral graph theory; Pancake flipping; Prefix reversal

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