Abstract
For a class of graphs we say that it is globally determined if any two nonisomorphic graphs from that class have nonisomorphic globals. We will prove that the class of so called CCB graphs and the class of finite forests are globally determined.
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References
K. A. Baker, G. F. McNulty, H. Werner: The finitely based varieties of graph algebras. Acta Sci. Math. 51 (1987), 3–15.
U. Baumann, R. Pöschel, I. Schmeichel: Power graphs. J. Inf. Process. Cybern. 30 (1994), 135–142. zbl
I. Bošnjak, R. Madarász: On power structures. Algebra Discrete Math. 2003 (2003), 14–35.
C. Brink: Power structures. Algebra Univers. 30 (1993), 177–216.
R. Diestel: Graph Theory. Graduate Texts in Mathematics 173, Springer, Berlin, 2000.
A. Drápal: Globals of unary algebras. Czech. Math. J. 35 (1985), 52–58.
R. Goldblatt: Varieties of complex algebras. Ann. Pure Appl. Logic 44 (1989), 173–242.
M. Gould, J. A. Iskra, C. Tsinakis: Globals of completely regular periodic semigroups. Semigroup Forum 29 (1984), 365–374.
J. Herchl, D. Jakubíková-Studenovská: Globals of unary algebras. Soft Comput. 11 (2007), 1107–1112. zbl doi
Y. Kobayashi: Semilattices are globally determined. Semigroup Forum 29 (1984), 217–222.
W. Korczyński: On a model of concurrent systems. Demonstr. Math. 30 (1997), 809–828.
W. Korczyński: Petri nets and power graphs—a comparison of two concurrence-models. Demonstr. Math. 31 (1998), 179–192.
L. Lovász: On the cancellation law among finite relational structures. Period. Math. Hung. 1 (1971), 145–156.
E. Lukács: Globals of G-algebras. Houston J. Math. 13 (1987), 241–244.
G. F. McNulty, C. R. Shallon: Inherently nonfinitely based finite algebras. Universal Algebra and Lattice Theory (R. S. Freese, O. C. Garcia, eds.). Lecture Notes in Mathematics 1004, Springer, Berlin, 1983, pp. 206–231.
E. M. Mogiljanskaja: Non-isomorphic semigroups with isomorphic semigroups of subsets. Semigroup Forum 6 (1973), 330–333.
C. R. Shallon: Non-finitely based binary algebras derived from lattices. Ph.D. Thesis, University of California, Los Angeles, 1979.
T. Tamura: On the recent results in the study of power semigroups. Semigroups and Their Applications (S.M. Goberstein, P.M. Higgins, eds.). Reidel Publishing Company, Dordrecht, 1987, pp. 191–200.
S. Whitney: Théories linéaries. Ph.D. Thesis, Université Laval, Québec, 1977.
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The research was supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia, Grant No. 174 018.
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Bošnjak, I., Madarász, R. Some globally determined classes of graphs. Czech Math J 68, 633–646 (2018). https://doi.org/10.21136/CMJ.2018.0552-16
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DOI: https://doi.org/10.21136/CMJ.2018.0552-16