Metrically regular square of metrically regular bipartite graphs of diameter D = 6

Vladimír Vetchý

Archivum Mathematicum (1993)

  • Volume: 029, Issue: 1-2, page 29-38
  • ISSN: 0044-8753

Abstract

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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].

How to cite

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Vetchý, Vladimír. "Metrically regular square of metrically regular bipartite graphs of diameter $D=6$." Archivum Mathematicum 029.1-2 (1993): 29-38. <http://eudml.org/doc/247430>.

@article{Vetchý1993,
abstract = {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].},
author = {Vetchý, Vladimír},
journal = {Archivum Mathematicum},
keywords = {spectra of graphs; square of graphs; bipartite graphs; metrically regular graphs; association scheme; spectra; metrically regular graphs; association scheme; bipartite graph; diameter; eigenvalues; adjacency matrix},
language = {eng},
number = {1-2},
pages = {29-38},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Metrically regular square of metrically regular bipartite graphs of diameter $D=6$},
url = {http://eudml.org/doc/247430},
volume = {029},
year = {1993},
}

TY - JOUR
AU - Vetchý, Vladimír
TI - Metrically regular square of metrically regular bipartite graphs of diameter $D=6$
JO - Archivum Mathematicum
PY - 1993
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 029
IS - 1-2
SP - 29
EP - 38
AB - 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].
LA - eng
KW - spectra of graphs; square of graphs; bipartite graphs; metrically regular graphs; association scheme; spectra; metrically regular graphs; association scheme; bipartite graph; diameter; eigenvalues; adjacency matrix
UR - http://eudml.org/doc/247430
ER -

References

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  1. Association Schemes I, Arch. Math. Brno 17 (1981), 173-184. (1981) Zbl0479.05020MR0672657
  2. Classification and analysis of partially balanced incomplete block design with two association classes, J. Amer. Stat. Assn. 47 (1952), 151-184. (1952) MR0048772
  3. On linear associative algebras corresponding to association schemes of partially balanced designs, Ann. Math. Statist. 30 (1959), 21-36. (1959) MR0102157
  4. Spectra of graphs, Deutscher Verlag der Wissenchaften, Berlin, 1980. (1980) 
  5. Über selbstkomplementäre Graphen, Publ. Math. Debrecen 9 (1962), 270-288. (1962) Zbl0119.18904MR0151953
  6. 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. (1970) Zbl0249.05136MR0266799
  7. Metrically regular square of metrically regular bigraphs I, Arch. Math. Brno 27b (1991), 183-197. (1991) MR1189214
  8. Metrically regular square of metrically regular bigraphs II, Arch. Math. Brno 28 (1992), 17-24. (1992) MR1201862

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