‎In this article we discuss examples of fractal $omega$-operads‎. ‎Thus we show that there is an $omega$-operadic approach to explain existence of‎ ‎the globular set of globular setsfootnote{Globular sets are also called $omega$-graphs by the French School.}‎, ‎the reflexive globular set of reflexive globular sets‎, ‎the $omega$-magma of $omega$-magmas‎, ‎and also the reflexive $omega$-magma ...

A simple graph is said to be reflexive if its second largest eigenvalue does not exceed 2. The property λ2 ≤ 2 is a hereditary one, i.e. any induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented by maximal graphs within a given class. Bicyclic graphs whose two cycles have a common path are called θ-graphs. We consider classes of m...

‎from hilbert's theorem of zeroes‎, ‎and from noether's ideal theory‎, ‎birkhoff derived certain algebraic concepts (as explained by tholen) that have a dual significance in general toposes‎, ‎similar to their role in the original examples of algebraic geometry‎. ‎i will describe a simple example that illustrates some of the aspects of this relationship‎. the dualization from algebra to geometr...

The spectrum of a graph is the family of eigenvalues of its (0, 1) adjacency matrix.A simple graph is reflexive if its second largest eigenvalue 2 does not exceed 2. The graphic property 2 2 is a hereditary one, i.e. every induced subgraph of a reflexive graph preserves this property and that is why reflexive graphs are usually represented through maximal graphs. Cacti, or treelike graphs, are ...

We describe a generating set for the variety of reflexive graphs that admit a compatible k-ary near-unanimity operation; we further delin-eate a very simple subset that generates the variety of j-absolute retracts; in particular we show that the class of reflexive graphs with a 4-NU operation coincides with the class of 3-absolute retracts. Our results generalise and encompass several results o...