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Identities in biregular leftmost graph varieties of type \((2,0)\). (English) Zbl 1201.08006

Summary: Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type \((2,0)\). We say that a graph \(G\) satisfies a term equation \(s \approx t\) if the corresponding graph algebra \(\underline{A(G)}\) satisfies \(s \approx t\). A class of graph algebras \(V\) is called a graph variety of \(V= \text{Mod}_g\Sigma\), where \(\Sigma\) is a subset of \(T(X) \times T(X)\). A graph variety \(V'= \text{Mod}_g\Sigma'\) is called a biregular leftmost graph variety if \(\Sigma'\) is a set of biregular leftmost term equations. A term equation \(s \approx t\) is called an identity in a variety \(V\) if \(G\) satisfies \(s \approx t\) for all \(G \in V\).
In this paper we characterize identities in each biregular leftmost graph variety. For identities, varieties and other basic concepts of universal algebra see, e.g., [K. Denecke and S. L. Wismath, Universal algebra and applications in theoretical computer science. Boca Raton, FL: Chapman & Hall (2002; Zbl 0993.08001)].

MSC:

08B15 Lattices of varieties
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)

Citations:

Zbl 0993.08001
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References:

[1] Denecke K., Universal Algebra and Applications in Theoretical Computer Science (2002)
[2] DOI: 10.4134/BKMS.2007.44.4.651 · Zbl 1142.08003 · doi:10.4134/BKMS.2007.44.4.651
[3] Kiss E. W., Acta Sci. Math. 54 pp 57–
[4] DOI: 10.7151/dmgaa.1014 · Zbl 0977.08006 · doi:10.7151/dmgaa.1014
[5] Poomsa-ard T., Thai Journal of Mathematics 2 pp 171–
[6] DOI: 10.7151/dmgaa.1091 · Zbl 1102.08004 · doi:10.7151/dmgaa.1091
[7] DOI: 10.1002/malq.19890350311 · Zbl 0661.03020 · doi:10.1002/malq.19890350311
[8] DOI: 10.1007/BF01189000 · Zbl 0725.08002 · doi:10.1007/BF01189000
[9] Pöschel R., Comment. Math. Univ. Carolonae 28 pp 581–
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