In this paper, we define the non-centralizer graph associated to a finite group G, as the graph whose vertices are the elements of G, and whose edges are obtained by joining two distinct vertices if their centralizers are not equal. We denote this graph by ΥG. The non-centralizer graph is used to study the properties of the non-commuting graph of an AC-group. We prove that the non-centralizer g...

INTRODUCTION Active commuting - walking and bicycling for travel to and/or from work or educational addresses - may facilitate daily, routine physical activity. Several studies have investigated the relationship between active commuting and commuting stress; however, there are no studies examining the relationship between solely bicycle commuting and perceived stress, or studies that account fo...

As a sustainable mode of travel, walking for transportation has multiple environmental, social, and health-related benefits. In existing studies, however, such rarely been differentiated between commuting non-commuting trips. Using multilevel zero-inflated negative binomial regression Tobit models, this study empirically examines the frequency duration their correlates in Xiamen, China. It find...

For a nilpotent group $G$, let $\Xi(G)$ be the difference between complement of generating graph $G$ and commuting with vertices corresponding to central elements removed. That is, has vertex set $G \setminus Z(G)$, two adjacent if only they do not commute generate $G$. Additionally, $\Xi^+(G)$ subgraph induced by its non-isolated vertices. We show that an edge, then is connected diameter $2$ o...

Let G be a abelian finite group. The non-commuting graph Δ(G) of G is defined as follows: The vertex set is G− Z(G), two vertex x and y are joined by an edge whenever xy = yx. Note that if G is abelian, then Δ(G) has no vertices. So, throughout this article let G be a nonabelian finite group. There are many papers on algebraic structure, using the properties of graphs, for instance see [4, 2, 3...

BACKGROUND: Children's active commuting to school, i.e. walking or cycling to school, was associated with greater moderate-to-vigorous physical activity, although studies among ethnic minorities are sparse. OBJECTIVES: Among a low-income, ethnic minority sample of fourth grade students from eight public schools, we examined (1) correlates of active commuting to school and (2) the relationship b...

We consider orbifoldings of the Moonshine Module with respect to the abelian group generated by a pair of commuting Monster group elements with one of prime order p = 2, 3, 5, 7 and the other of order pk for k = 1 or k prime. We show that constraints arising from meromorphic orbifold conformal field theory allow us to demonstrate that each orbifold partition function with rational coefficients ...