Geodesic
Metrically regular square of metrically regular bipartite graphs of diameter $D=6$
Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 29-38 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter $D = 6$ (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter $D 6$ see [7] and [8].
The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter $D = 6$ (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter $D 6$ see [7] and [8].
Classification : 05C50, 05C75, 05E30
Keywords: spectra of graphs; square of graphs; bipartite graphs; metrically regular graphs; association scheme 
@article{ARM_1993_29_1-2_a5,
     author = {Vetch\'y, Vladim{\'\i}r},
     title = {Metrically regular square of metrically regular bipartite graphs of diameter $D=6$},
     journal = {Archivum mathematicum},
     pages = {29--38},
     year = {1993},
     volume = {29},
     number = {1-2},
     mrnumber = {1242626},
     zbl = {0797.05060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a5/}
}
TY  - JOUR
AU  - Vetchý, Vladimír
TI  - Metrically regular square of metrically regular bipartite graphs of diameter $D=6$
JO  - Archivum mathematicum
PY  - 1993
SP  - 29
EP  - 38
VL  - 29
IS  - 1-2
UR  - http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a5/
LA  - en
ID  - ARM_1993_29_1-2_a5
ER  - 
%0 Journal Article
%A Vetchý, Vladimír
%T Metrically regular square of metrically regular bipartite graphs of diameter $D=6$
%J Archivum mathematicum
%D 1993
%P 29-38
%V 29
%N 1-2
%U http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a5/
%G en
%F ARM_1993_29_1-2_a5
Vetchý, Vladimír. Metrically regular square of metrically regular bipartite graphs of diameter $D=6$. Archivum mathematicum, Tome 29 (1993) no. 1-2, pp. 29-38. http://geodesic.mathdoc.fr/item/ARM_1993_29_1-2_a5/

[1] Bauer, L.: Association Schemes I. Arch. Math. Brno 17 (1981), 173-184. | MR | Zbl

[2] Bose, R. C., Shimamoto, T.: Classification and analysis of partially balanced incomplete block design with two association classes. J. Amer. Stat. Assn. 47 (1952), 151-184. | MR

[3] Bose, R. C., Messner, D. M.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Statist. 30 (1959), 21-36. | MR

[4] Cvetković, D. M., Doob, M., Sachs, H.: Spectra of graphs. Deutscher Verlag der Wissenchaften, Berlin, 1980.

[5] Sachs, H.: Über selbstkomplementäre Graphen. Publ. Math. Debrecen 9 (1962), 270-288. | MR | Zbl

[6] Smith, J. H.: Some properties of the spectrum of a graph. Comb.Struct. and their Applic., Gordon and Breach, Sci. Publ. Inc., New York-London-Paris (1970), 403-406. | MR | Zbl

[7] Vetchý, V.: Metrically regular square of metrically regular bigraphs I. Arch. Math. Brno 27b (1991), 183-197. | MR

[8] Vetchý, V.: Metrically regular square of metrically regular bigraphs II. Arch. Math. Brno 28 (1992), 17-24. | MR