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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. V. Avgustinovich
AU  - E. V. Gorkunov
AU  - Yu. D. Syomina
TI  - On antipodal properties for eigenfunctions of graphs
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2015
SP  - 862
EP  - 867
VL  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2015_12_a57/
LA  - ru
ID  - SEMR_2015_12_a57
ER  - 
%0 Journal Article
%A S. V. Avgustinovich
%A E. V. Gorkunov
%A Yu. D. Syomina
%T On antipodal properties for eigenfunctions of graphs
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2015
%P 862-867
%V 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2015_12_a57/
%G ru
%F SEMR_2015_12_a57
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/

[1] S. V. Avgustinovich, “Ob odnom svoistve sovershennykh binarnykh kodov”, Diskret. analiz i issled. oper., Ser. 1, 2:1 (1995), 4–6 | Zbl

[2] N. N. Tokareva, “O verkhnei otsenke chisla ravnomerno upakovannykh dvoichnykh kodov”, Diskret. analiz i issled. oper., 14:3 (2007), 90–97

[3] A. L. Andrew, “Eigenvectors of certain matrices”, Linear Algebra Its Appl., 7:2 (1973), 151–162 | DOI | MR | Zbl

[4] D. M. Cvetković, M. Doob, H. Sachs, Spectra of Graphs: Theory and Application, VEB Deutscher Verlag Wissenschaften, 1980 | MR | Zbl

[5] D. S. Krotov, “On weight distributions of perfect colorings and completely regular codes”, Des. Codes Cryptogr., 61:3 (2011), 315–329 | DOI | MR | Zbl

[6] D. Stevanović, “Antipodal graphs of small diameter”, Filomat, 15 (2001), 79–83 | MR | Zbl