arXiv subjects

Montserrat Maureso

Publications and source records attributed to Montserrat Maureso.

3 recordsLinked to original sources

arXiv2019

Metric dimension of maximal outerplanar graphs

In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if $β(G)$ is the metric dimension of a maximal outerplanar graph $G$ of order $n$, we prove that $2\le β(G) \le \lceil \frac{2n}{5}\rceil$ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of $G$ is 2 and to build a resolving set of size $\lceil \frac{2n}{5}\rceil$ for $G$. Moreover, we characterize the maximal outerplanar graphs with metric dimension 2.

math.CO↗

arXiv2017

Steinhaus Triangles Generated by Vectors of the Canonical Bases

We give a method to calculate the weight of binary Steinhaus triangles generated by the vectors of the canonical basis of the vector space $\mathbb{F}_2^n$ over the field $\mathbb{F}_2$ of order $2$.

math.CO↗

arXiv2017

Small and Large Weights in Steinhaus Triangles

Let $\{0=w_0<w_1<w_2<\ldots<w_m\}$ be the set of weights of binary Steinhaus triangles of size $n$, and let $W_i$ be the set of sequences in $\mathbb{F}_2^n$ that generate triangles of weight $w_i$. We obtain the values of $w_i$ and the corresponding sets $W_i$ for $i\in\{1,2,3,m\}$, and partial results about $w_{m-1}$ and $W_{m-1}$.

math.CO↗