A construction of cospectral graphs for the normalized Laplacian

Details A construction of cospectral graphs for the normalized Laplacian A construction of cospectral graphs for the normalized Laplacian

2010-08-21

arxiv.org/abs/1008.3646v2

S. Butler and J. Grout, A construction of cospectral graphs for the normalized Laplacian, Electronic Journal of Combinatorics

Mathematics

Combinatorics

21 pages; lots of figures; includes SAGE code

Scientific paper

We give a method to construct cospectral graphs for the normalized Laplacian by a local modification in some graphs with special structure. Namely, under some simple assumptions, we can replace a small bipartite graph with a cospectral mate without changing the spectrum of the entire graph. We also consider a related result for swapping out biregular bipartite graphs for the matrix $A+tD$. We produce (exponentially) large families of non-bipartite, non-regular graphs which are mutually cospectral, and also give an example of a graph which is cospectral with its complement but is not self-complementary.

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