Geodesic
Non-isomorphic graphs with cospectral symmetric powers
The electronic journal of combinatorics, Tome 16 (2009) no. 1
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The symmetric $m$-th power of a graph is the graph whose vertices are $m$-subsets of vertices and in which two $m$-subsets are adjacent if and only if their symmetric difference is an edge of the original graph. It was conjectured that there exists a fixed $m$ such that any two graphs are isomorphic if and only if their $m$-th symmetric powers are cospectral. In this paper we show that given a positive integer $m$ there exist infinitely many pairs of non-isomorphic graphs with cospectral $m$-th symmetric powers. Our construction is based on theory of multidimensional extensions of coherent configurations.
DOI : 10.37236/209
Classification : 05C50, 05C60, 05E30 
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     author = {Amir Rahnamai Barghi and Ilya Ponomarenko},
     title = {Non-isomorphic graphs with cospectral symmetric powers},
     journal = {The electronic journal of combinatorics},
     year = {2009},
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Amir Rahnamai Barghi; Ilya Ponomarenko. Non-isomorphic graphs with cospectral symmetric powers. The electronic journal of combinatorics, Tome 16 (2009) no. 1. doi: 10.37236/209

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