The commuting graph C(G,X), where G is a group and X is a subset of G, is the graph with vertex set X and distinct vertices being joined by an edge whenever they commute. Here the diameter of C(G,X) is studied when G is a symmetric group and X a conjugacy class of elements of order 3.

Let G be a finite non-abelian group and Z(G) its center. We associate commuting graph $$\Gamma (G)$$ to G, whose vertex set is $$G\setminus Z(G)$$ two distinct vertices are adjacent if they commute. In this paper we prove that the of all groups has maximum degree bounded above by fixed $$k \in {\mathbb {N}}$$ finite. Also, characterize for which associated graphs have at most 4.

With the development of information and communications technology, user-generated content and crowdsourced data are playing a large role in studies of transport and public health. Recently, Strava, a popular website and mobile app dedicated to tracking athletic activity (cycling and running), began offering a data service called Strava Metro, designed to help transportation researchers and urba...

We study the commuting graph on elements of odd prime order in finite simple groups. The results are used in a forthcoming paper describing the structure of Bruck loops and Bol loops of exponent 2.

"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...

The increasing travel demands and the growing diversity of trip purposes in megacities are placing more pressure on the urban transportation system, and there is an urgent need to popularize public transportation and control the exploding increase in travels by private cars. In order to enhance the competence of public transportation and establish a balance among various travel modes in megacit...