Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
spectra of graphs; squares of graphs; distance regular graphs; association scheme; metrically regular graphs; bipartite graphs; Kneser graph
spectra of graphs; squares of graphs; distance regular graphs; association scheme; metrically regular graphs; bipartite graphs; Kneser graph
Summary:
The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only two tables of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter $D = 7$ (8 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter $D < 7$ see [8], [9] and [10].
References:
[1] Bannai, E, Ito, T.: Algebraic Combinatorics I. The Bejamin/Cummings Publishing Company, California, 1984. MR 0882540
[2] Barile, M., Weisstein, E.W.: Kneser Graph. From MathWorld-A Wolfram Web Resource, http://mathworld.wolfram.com/KneserGraph.html
[3] Bose, R.C., Shimamoto, T.: Classification and analysis of partially balanced incomplete block design with two association classes. J. Amer. Statist. Assoc. 47 (1952), 151–184. DOI 10.1080/01621459.1952.10501161 | MR 0048772
[4] Bose, R.C., Shimamoto, T.: On linear associative algebras corresponding to association schemes of partially balanced designs. Ann. Math. Statist. 30 (1959), 21–36. DOI 10.1214/aoms/1177706356 | MR 0102157
[5] Cvetković, D.M., Doob, M., Sachs, H.: Spectra of graphs. Deutscher Verlag der Wissenchaften, Berlin, 1980. MR 0690768
[6] Sachs, H.: Über selbstkomplement are Graphen. Publ. Math. Debrecen 9 (1962), 270–288. MR 0151953
[7] Smith, J.H.: Some properties of the spectrum of a graph. Comb.Struct. and their Applications, Gordon and Breach, Sci. Publ. Inc., New York-London-Paris, 1970, pp. 403–406. MR 0266799 | Zbl 0249.05136
[8] Vetchý, V.: Metrically regular square of metrically regular bigraphs I. Arch. Math. (Brno) 27b (1991), 183–197. MR 1189214
[9] Vetchý, V.: Metrically regular square of metrically regular bigraphs II. Arch. Math. (Brno) 28 (1992), 17–24. MR 1201862
[10] Vetchý, V.: Metrically regular square of metrically regular bipartite graphs of diameter $D=6$. Arch. Math. (Brno) 29 (1993), 29–38. MR 1242626
Search
Partner of
