A cospectral family of graphs for the normalized Laplacian found by toggling
نویسندگان
چکیده
منابع مشابه
A cospectral family of graphs for the normalized Laplacian found by toggling
We give a construction of a family of (weighted) graphs that are pairwise cospectral with respect to the normalized Laplacian matrix, or equivalently probability transition matrix. This construction can be used to form pairs of cospectral graphs with differing number of edges, including situations where one graph is a subgraph of the other. The method used to demonstrate cospectrality is by sho...
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A characteristic of the normalized Laplacian matrix is the possibility for cospectral graphs which do not have the same number of edges. We give a construction of an infinite family of weighted graphs that are pairwise cospectral and which can be transformed into simple graphs. In particular, some of these graphs are cospectral with subgraphs of themselves. In the proof we deconstruct these gra...
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We give a method to construct cospectral graphs for the normalized Laplacian by swapping edges between vertices in some special graphs. We also give a method to construct an arbitrarily large family of (non-bipartite) graphs which are mutually cospectral for the normalized Laplacian matrix of a graph. AMS 2010 subject classification: 05C50
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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 p...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.06.033