82 research outputs found
Unicyclic Graphs with equal Laplacian Energy
We introduce a new operation on a class of graphs with the property that the
Laplacian eigenvalues of the input and output graphs are related. Based on this
operation, we obtain a family of order (square root of n) noncospectral
unicyclic graphs on n vertices with the same Laplacian energy.Comment: 11 pages, 11 figures, slightly modified version of Theorem 1 when
compared with original pape
Limits of permutation sequences
A permutation sequence is said to be convergent if the density of occurrences
of every fixed permutation in the elements of the sequence converges. We prove
that such a convergent sequence has a natural limit object, namely a Lebesgue
measurable function with the additional properties that,
for every fixed , the restriction is a cumulative
distribution function and, for every , the restriction
satisfies a "mass" condition. This limit process is well-behaved:
every function in the class of limit objects is a limit of some permutation
sequence, and two of these functions are limits of the same sequence if and
only if they are equal almost everywhere. An ingredient in the proofs is a new
model of random permutations, which generalizes previous models and might be
interesting for its own sake.Comment: accepted for publication in the Journal of Combinatorial Theory,
Series B. arXiv admin note: text overlap with arXiv:1106.166
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