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A Cheeger inequality for the lower spectral gap
Let be a Cayley graph, or a Cayley sum graph, or a twisted Cayley
graph, or a twisted Cayley sum graph, or a vertex-transitive graph. Denote the
degree of by , its edge Cheeger constant by ,
and its vertex Cheeger constant by . Assume that is
undirected, non-bipartite. We prove that the edge bipartiteness constant of
is , the vertex bipartiteness
constant of is , and the smallest eigenvalue of the
normalized adjacency operator of is .
This answers in the affirmative a question of Moorman, Ralli and Tetali on the
lower spectral gap of Cayley sum graphs
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