Geodesic
On antipodal properties for eigenfunctions of graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 862-867

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A graph $G=(V,E)$ of diameter $d$ is termed to be antipodal if for any vertex $x\in{V}$ there is precisely one another $x^\prime\in{V}$ such that $d(x,x^\prime)=d$. In addition, an antipodal graph is called rigid if for any pair of its antipodal vertices $x,x^\prime\in{V}$ and any third vertex $y\in{V}$ the equality $d(x,x^\prime)=d(x,y)+d(y,x^\prime)$ holds. In this paper eigenfunctions of rigid antipodal graphs are investigated. It is shown that every homogeneous eigenfunction of such a graph with odd diameter is determined uniquely from its values on vertices in two middle layers of the graph.
Keywords: antipodality, eigenfunction of a graph.
Mots-clés : antipodal graph 
@article{SEMR_2015_12_a57,
     author = {S. V. Avgustinovich and E. V. Gorkunov and Yu. D. Syomina},
     title = {On antipodal properties for eigenfunctions of graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {862--867},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a57/}
}
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S. V. Avgustinovich; E. V. Gorkunov; Yu. D. Syomina. On antipodal properties for eigenfunctions of graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 862-867. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a57/