In this paper, we calculate diameters of connected components of commuting graphs of GLn(S), for an integer n ≥ 2 and a commutative antinegative entire semiring S, unless n is a non-prime odd number and S has at least two invertible elements.

In this paper, diameters of connected components of commuting graphs of GLn(S) are calculated, for an integer n ≥ 2 and a commutative antinegative entire semiring S, unless n is a non-prime odd number and S has at least two invertible elements.

For a group G and X a subset of G the commuting graph of G on X, denoted by C(G,X), is the graph whose vertex set is X with x, y ∈ X joined by an edge if x 6= y and x and y commute. If the elements in X are involutions, then C(G,X) is called a commuting involution graph. This paper studies C(G,X) when G is a 3-dimensional projective special unitary group and X a G-conjugacy class of involutions...

We present a two-parameter family (Gm,k)m,k∈N≥2 , of finite, non-abelian random groups and propose that, for each fixed k, as m → ∞ the commuting graph of Gm,k is almost surely connected and of diameter k. We present heuristic arguments in favour of this conjecture, following the lines of classical arguments for the Erdős– Rényi random graph. As well as being of independent interest, our groups...

"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...

Abstract Suppose that G is a finite group and X -conjugacy classes of involutions. The commuting involution graph $${\mathcal {C}}(G,X)$$ C ( G , X ) the whose vertex set with $$x, y \in X$$ x</...

We used participant-produced photography to investigate everyday commuting practices in Cambridge, UK. Photovoice served as an observational method for producing ethnographically rich data. A total of 19 participants produced over 500 photos about their journeys to and from work and took part in photo-elicitation interviews. Three themes emerged. First, many images depicted 'well-being' in comm...