članak: 1 od 1  
Applicable Analysis and Discrete Mathematics
2007, br. 18, str. 59-63
jezik rada: engleski
neklasifikovan
doi:10.2298/PETF0718059H
There are integral trees of diameter 7
(naslov ne postoji na srpskom)
Híc Pavel, Pokorný Milan
Department of Mathematics and Computer Science, Faculty of Education, Trnava University, Trnava, Slovakia

e-adresa: phic@truni.sk, mpokorny@truni.sk

Sažetak

(ne postoji na srpskom)
A graph G is called integral if all the roots of the characteristic polynomial P(G; x) are integers. In this paper, four integral trees of diameter 7 are given. These integral trees are the first integral trees of diameter 7 which have been found so far.

Ključne reči

integral tree; diameter; divisor; characteristic polynomial

Reference

CrossRef9Scindeks

Balinska, K.T., Cvetković, D.M., Radosavljević, Z.S., Simić, S.K., Stevanović, D.P. (2002) A survey on integral graphs. Publikacija Elektrotehničkog fakulteta - serija: matematika, br. 13, str. 42-65

VBS226

Cvetković, D.M., Doob, M., Sachs, H. (1980) Spectra of graphs: Theory and application. New York: Academic Press

4

Harary, F., Schwenk, A.J. (1974) Which graphs have integral spectra?. u: R.Bari and F.Harary (ur.) Graphs and Combinatorics (Lecture Notes in Mathematics, 406), Berlin, itd: Springer Verlag, 45-51

48

Harary, F. (1969) Graph theory. Reading, MA, itd: Addison-Wesley

MathSciNetKoBSON2

Hic, P., Nedela, R. (1998) Balanced integral trees. Math. Slovaca, 48, 5, 429-445

Hic, P., Nedela, R. (1996) Note on zeros of the characteristic polynomial of balanced trees. Acta Univ. M. Bellii Math, br. 3, 31-35

MathSciNetKoBSON2

Hic, P., Nedela, R., PavlikovA, S. (1992) Front-divisors of trees. Acta Math. Univ. Comenianae, 61, 1, 69-84

1

Hic, P., PavlikovA, S. (1995) Integral bibalanced trees. u: The collection of papers of the Faculty of materials science and technology, Trnava, vol. 3, 227-233

Hic, P., Pokorny, M. (2003) On integral balanced rooted tree of diameter 10. Acta Univ. Mathaei Belii, Series Mathematics, br. 10, 9-15

Pokorny, M. (2004) A note on integral balanced rooted trees of diameter 10. Acta Fac. Paed. Univ. Tyrnaviensis, Ser. C, br. 8, 13-15

Pokorny, M. (2002) Integral trees and Pell's equations. Acta Fac. Paed. Univ. Tyrnaviensis, Ser. C, br. 6, 44-50

1

Wang, L.G. (2005) A survey of results on integral trees and integral graphs. Twente, Memorandum br. 1763

Wang, L.G. (2005) Integral trees and integral graphs. Enschede: Wöhrmann Print Service

KoBSON

Wang, L.G., Li, X.L. (2005) Integral trees with diameter 5 and 6. Discrete Mathematics, 297 (1-3), 128-143

KoBSON

Wang, L.G., Li, X.L., Zhang, S.G. (2004) Families of integral trees with diameter 4, 6, and 8. Discrete Applied Mathematics, 136, 349-362