A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

"This paper analyses whether the basic monocentric model of urban structure and commuting explains actual commuting in Europe, i.e. The Netherlands. As in the USA much wasteful commuting is established. The basic model has a low degree of explanatory power. In order to get more in line with actual commuting, the paper elaborates two alternatives to the basic model. Besides a deconcentrated mode...

Let $G$ be a non-abelian group. The non-commuting graph $Gamma_G$ of $G$ is defined as the graph whose vertex set is the non-central elements of $G$ and two vertices are joined if and only if they do not commute.In this paper we study some properties of $Gamma_G$ and introduce $n$-regular $AC$-groups. Also we then obtain a formula for Szeged index of $Gamma_G$ in terms of $n$, $|Z(G)|$ and $|G|...

A comprehensive graph theoretical and finite geometrical study of the commutation relations between the generalized Pauli operators of N -qudits is performed in which vertices/points correspond to the operators and edges/lines join commuting pairs of them. As per two-qubits, all basic properties and partitionings of the corresponding Pauli graph are embodied in the geometry of the generalized q...

Active commuting provides routine-based regular physical activity which can reduce the risk of chronic diseases. Using public transportation involves some walking or cycling to a transit stop, transfers and a walk to the end location and users of public transportation have been found to accumulate more moderate physical activity than non-users. Understanding how public transportation characteri...

Eilenberg has shown that there is a one-to-one correspondence between varieties of finite monoids and varieties of recognizable languages. In this paper, we give a description of a variety of languages close to the class of piecewise testable languages considered by I. Simon. The corresponding variety of monoids is the variety of J -trivial monoids with commuting idempotents. This result is the...