Geodesic
Isospectral genus two graphs are isomorphic
Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 223-235.

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By a graph we mean a finite connected multigraph without bridges. The genus of a graph is the dimension of its homology group. Two graphs are isospectral is they share the same Laplacian spectrum. We prove that two genus two graphs are isospectral if and only if they are isomorphic. Also, we present two bridgeless genus three graphs that are not isomorphic. The paper is motivated by the following open problem posed by Peter Buser: are isospectral Riemann surfaces of genus two isometric?
DOI : 10.26493/1855-3974.550.e1a
Keywords: Graph, Laplacian spectrum, isospectral graphs, Laplacian polynomial, spanning tree 
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Alexander D. Mednykh; Ilya A. Mednykh. Isospectral genus two graphs are isomorphic. Ars Mathematica Contemporanea, Tome 10 (2016) no. 2, pp. 223-235. doi : 10.26493/1855-3974.550.e1a. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.550.e1a/

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