Geodesic
A construction of cospectral graphs for the normalized Laplacian
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/718
Classification : 05C50
Mots-clés : normalized Laplacian, cospectral, bipartite subgraph swapping 
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     author = {Steve Butler and Jason Grout},
     title = {A construction of cospectral graphs for the normalized {Laplacian}},
     journal = {The electronic journal of combinatorics},
     year = {2011},
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     number = {1},
     doi = {10.37236/718},
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Steve Butler; Jason Grout. A construction of cospectral graphs for the normalized Laplacian. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/718

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