Geodesic
On the minimum supports of some eigenfunctions in the Doob graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 258-266

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We prove that the minimum size of the support of an eigenfunction in the Doob graph $D(m,n)$ corresponding to the second largest eigenvalue is $6 \cdot 4^{2m+n-2}$, and obtain characterisation of all eigenfunctions with minimum support. Similar results, with the minimum support size $2^{2m+n}$, are obtained for the minimum eigenvalue of $D(m,n)$.
Keywords: eigenfunction, minimum support, Doob graph. 
@article{SEMR_2018_15_a64,
     author = {E. A. Bespalov},
     title = {On the minimum supports of some eigenfunctions in the {Doob} graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {258--266},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a64/}
}
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E. A. Bespalov. On the minimum supports of some eigenfunctions in the Doob graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 258-266. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a64/