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The diameters of the graphs of semirings

Published online by Cambridge University Press:  09 April 2009

J. S. Ratti  and
Y.-F. Lin
J. S. Ratti
Affiliation:
University of South FloridaTampa, Florida
Y.-F. Lin
Affiliation:
University of South FloridaTampa, Florida
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Let be a family of sets, {Fa|α∈Λ}. By the graph G of the system , we mean the graph whose set of vertices is and in which the vertices Fβ∈, are adjacent (that is, are joined by an edge) if and only if Fα ≠ Fβ and Fα ∩ Fβ □, where □denotes the empty set.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 4 , November 1970 , pp. 433 - 440
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Bosák, J., The graphs of semigroups, theory of graphs, and its applications Proc. Symp. Graph Theory, Smolenice 1 (963), Academic Press (1965), pp. 119–125.Google Scholar
[2]Lin, Y-F., ‘A problem of Bosák concerning the graphs of semigroups’, Proc. American Math. Society 21 (1969), 343–346.Google Scholar
[3]Lin, Y.-F. and Ratti, J. S., ‘The graphs of semirings’, Journal of Algebra 14 (1970), 73–82.CrossRefGoogle Scholar