Abstract
We study the proposed L.M. Martynov, the rank of a planarity for varieties of commutative semigroups.
Highlights
Continuing the series of papers [1]-[5] on the proposed L.M.Martynovs Program for the Study of the planarity of Cayley graphs for varieties of semigroups, in this article we consideration not exposed earlier studies semigroup variety.Recall that a variety V of semigroups is ranked planarity r, where r is the natural number, if all the V-free semigroup of rank ≤ r admits a planar Cayley graph, and V-free semigroup of rank r + 1 does not allow planar Cayley graph
The Cayley graph Cay(G,S) of G relative to S is defined as the graph with vertex set G and edge set E(S) consisting of those ordered pairs (x,y) such that sx=y for some s∈S” Definition 2
Martynov for in posing the problem, constant attention to this work and useful discussions. We found another planar manifold defined by the identity properties {xy = x2; xyz = xy}, and formulated the hypothesis that the only listed semigroup variety planar
Summary
Continuing the series of papers [1]-[5] on the proposed L.M.Martynovs Program for the Study of the planarity of Cayley graphs for varieties of semigroups, in this article we consideration not exposed earlier studies semigroup variety. Recall that a variety V of semigroups is ranked planarity r, where r is the natural number, if all the V-free semigroup of rank ≤ r admits a planar Cayley graph, and V-free semigroup of rank r + 1 does not allow planar Cayley graph. If for a variety V of the natural number r does not exist, V semigroups has infinite rank planarity [5]. Each semigroup which admits a planar Cayley graph, called planar
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