L’efecte de les intervencions escolars en la promoció d’activitat física

L’entorn escolar és considerat el més adequat per implementar-hi intervencions que contrarestin la inactivitat física, tot i que encara hi ha controvèrsia sobre quina és la millor estratègia. L’objectiu d’aquest article va ser revisar d’una manera sistemàtica les intervencions escolars actuals en la promoció de l’activitat física. Varen ser inclosos en la revisió estudis controlats i aleatoritzats duts a terme a les escoles, que haguessin inclòs alguna mesura d’activitat física o de condició física i en els quals haguessin participat nins de sis a dotze anys, i que foren publicats entre els anys 2007 i 2012. En aquesta revisió, entre el 70-80% dels estudis varen ser efectius. La intervenció basada en la combinació de diferents components va ser l’estratègia més consistent.School-based interventions are thought to be the most appropriate, effective way of counteracting low physical activity, although controversy surrounds what the best strategy is. This paper aims to make a systematic review of current interventions in schools. Random controlled trials in schools with some resulting measurement of physical activity or fitness were reviewed, using a population aged 6 to12 and studies published from 2007 to 2012. In the review, 70 to 80% of the trials were found to be effective. The most consistent intervention strategy was based on combination of different components

On the super edge-magicness of graphs with a specific degree sequence

A graph $G$ is said to be super edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}$ such that $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$ and $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant for each $uv\in E\left( G\right)$. In this paper, we study the super edge-magicness of graphs of order $n$ with degree sequence $s:4, 2, 2, \ldots, 2$. We also investigate the super edge-magic properties of certain families of graphs. This leads us to propose some open problems

Non-isomorphic graphs with common degree sequences

For all positive even integers $n$, graphs of order $n$ with degree sequence \begin{equation*} S_{n}:1,2,\dots,n/2,n/2,n/2+1,n/2+2,\dots,n-1 \end{equation*} naturally arose in the study of a labeling problem in \cite{IMO}. This fact motivated the authors of the aforementioned paper to study these sequences and as a result of this study they proved that there is a unique graph of order $n$ realizing $S_{n}$ for every even integer $n$. The main goal of this paper is to generalize this result

Some results concerning the valences of (super) edge-magic graphs

A graph $G$ is called edge-magic if there exists a bijective function $f:V\left(G\right) \cup E\left(G\right)\rightarrow \left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert +\left\vert E\left( G\right) \right\vert \right\}$ such that $f\left(u\right) + f\left(v\right) + f\left(uv\right)$ is a constant (called the valence of $f$) for each $uv\in E\left( G\right)$. If $f\left(V \left(G\right)\right) =\left\{1, 2, \ldots , \left\vert V\left( G\right) \right\vert \right\}$, then $G$ is called a super edge-magic graph. A stronger version of edge-magic and super edge-magic graphs appeared when the concepts of perfect edge-magic and perfect super edge-magic graphs were introduced. The super edge-magic deficiency $\mu_{s}\left(G\right)$ of a graph $G$ is defined to be either the smallest nonnegative integer $n$ with the property that $G \cup nK_{1}$ is super edge-magic or $+ \infty$ if there exists no such integer $n$. On the other hand, the edge-magic deficiency $\mu\left(G\right)$ of a graph $G$ is the smallest nonnegative integer $n$ for which $G\cup nK_{1}$ is edge-magic, being $\mu\left(G\right)$ always finite. In this paper, the concepts of (super) edge-magic deficiency are generalized using the concepts of perfect (super) edge-magic graphs. This naturally leads to the study of the valences of edge-magic and super edge-magic labelings. We present some general results in this direction and study the perfect (super) edge-magic deficiency of the star $K_{1,n}$

A method to compute the strength using bounds

A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\{1,2, \ldots, n \}$ to the vertices of $G$. The strength $\mathrm{str}\left(G\right)$ of $G$ is defined by $\mathrm{str}\left( G\right) =\min \left\{ \mathrm{str}_{f}\left( G\right)\left\vert f\text{ is a numbering of }G\right. \right\}$, where $\mathrm{str}_{f}\left( G\right) =\max \left\{ f\left( u\right) +f\left( v\right) \left\vert uv\in E\left( G\right) \right. \right\}$. A few lower and upper bounds for the strength are known and, although it is in general hard to compute the exact value for the strength, a reasonable approach to this problem is to study for which graphs a lower bound and an upper bound for the strength coincide. In this paper, we study general conditions for graphs that allow us to determine which graphs have the property that lower and upper bounds for the strength coincide and other graphs for which this approach is useless