Geodesic
A Formula for the Spectra of Differential Operators on Graphs
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 17-23

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We consider a connected undirected finite graph and a spectral problem generated by the double differentiation of functions on its edges (under usual conditions on the vertices ensuring the self-adjointness of the problem). We introduce, in a standard way, an entire function vanishing at the nonzero eigenvalues of the problem and give an explicit formula for this function, which involves graphs (introduced by V. I. Arnold) generated by a self-mapping of a finite set.
Keywords: differential operators, graph, cycle, tree.
Mots-clés : spectra 
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     title = {A {Formula} for the {Spectra} of {Differential} {Operators} on {Graphs}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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R. S. Ismagilov. A Formula for the Spectra of Differential Operators on Graphs. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 17-23. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a2/