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Families of strongly projective graphs

Benoit Larose (2002)

Discussiones Mathematicae Graph Theory

We give several characterisations of strongly projective graphs which generalise in many respects odd cycles and complete graphs [7]. We prove that all known families of projective graphs contain only strongly projective graphs, including complete graphs, odd cycles, Kneser graphs and non-bipartite distance-transitive graphs of diameter d ≥ 3.

Four-part semigroups - semigroups of Boolean operations

Prakit Jampachon, Yeni Susanti, Klaus Denecke (2012)

Discussiones Mathematicae - General Algebra and Applications

Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.

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