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The first generation of ELT instruments includes an optical-infrared high-resolution spectrograph, indicated as ELT-HIRES and recently christened ANDES (ArmazoNes high Dispersion Echelle Spectrograph). ANDES consists of three fibre-fed spectrographs ([U]BV, RIZ, YJH) providing a spectral resolution of $\sim$100,000 with a minimum simultaneous wavelength coverage of 0.4-1.8 $\mu$m with the goal of extending it to 0.35-2.4 $\mu$m with the addition of a U arm to the BV spectrograph and a separate K band spectrograph. It operates both in seeing- and diffraction-limited conditions and the fibre feeding allows several, interchangeable observing modes including a single conjugated adaptive optics module and a small diffraction-limited integral field unit in the NIR. Modularity and fibre-feeding allow ANDES to be placed partly on the ELT Nasmyth platform and partly in the Coud\'e room. ANDES has a wide range of groundbreaking science cases spanning nearly all areas of research in astrophysics and even fundamental physics. Among the top science cases, there are the detection of biosignatures from exoplanet atmospheres, finding the fingerprints of the first generation of stars, tests on the stability of Nature's fundamental couplings, and the direct detection of the cosmic acceleration. The ANDES project is carried forward by a large international consortium, composed of 35 Institutes from 13 countries, forming a team of almost 300 scientists and engineers which include the majority of the scientific and technical expertise in the field that can be found in ESO member states., Comment: SPIE astronomical telescope and instrumentation 2024, in press

A graph $G$ admiting a $2$-factor is \textit{pseudo $2$-factor isomorphic} if the parity of the number of cycles in all its $2$-factors is the same. In [M. Abreu, A.A. Diwan, B. Jackson, D. Labbate and J. Sheehan. Pseudo $2$-factor isomorphic regular bipartite graphs. Journal of Combinatorial Theory, Series B, 98(2) (2008), 432-444.] some of the authors of this note gave a partial characterisation of pseudo $2$-factor isomorphic bipartite cubic graphs and conjectured that $K_{3,3}$, the Heawood graph and the Pappus graph are the only essentially $4$-edge-connected ones. In [J. Goedgebeur. A counterexample to the pseudo $2$-factor isomorphic graph conjecture. Discr. Applied Math., 193 (2015), 57-60.] Jan Goedgebeur computationally found a graph $\mathscr{G}$ on $30$ vertices which is pseudo $2$-factor isomorphic cubic and bipartite, essentially $4$-edge-connected and cyclically $6$-edge-connected, thus refuting the above conjecture. In this note, we describe how such a graph can be constructed from the Heawood graph and the generalised Petersen graph $GP(8,3)$, which are the Levi graphs of the Fano $7_3$ configuration and the M\"obius-Kantor $8_3$ configuration, respectively. Such a description of $\mathscr{G}$ allows us to understand its automorphism group, which has order $144$, using both a geometrical and a graph theoretical approach simultaneously. Moreover we illustrate the uniqueness of this graph.

ESPRESSO is the new high-resolution spectrograph of ESO's Very-Large Telescope (VLT). It was designed for ultra-high radial-velocity precision and extreme spectral fidelity with the aim of performing exoplanet research and fundamental astrophysical experiments with unprecedented precision and accuracy. It is able to observe with any of the four Unit Telescopes (UT) of the VLT at a spectral resolving power of 140,000 or 190,000 over the 378.2 to 788.7 nm wavelength range, or with all UTs together, turning the VLT into a 16-m diameter equivalent telescope in terms of collecting area, while still providing a resolving power of 70,000. We provide a general description of the ESPRESSO instrument, report on the actual on-sky performance, and present our Guaranteed-Time Observation (GTO) program with its first results. ESPRESSO was installed on the Paranal Observatory in fall 2017. Commissioning (on-sky testing) was conducted between December 2017 and September 2018. The instrument saw its official start of operations on October 1st, 2018, but improvements to the instrument and re-commissioning runs were conducted until July 2019. The measured overall optical throughput of ESPRESSO at 550 nm and a seeing of 0.65 arcsec exceeds the 10% mark under nominal astro-climatic conditions. We demonstrate a radial-velocity precision of better than 25 cm/s during one night and 50 cm/s over several months. These values being limited by photon noise and stellar jitter show that the performanceis compatible with an instrumental precision of 10 cm/s. No difference has been measured across the UTs neither in throughput nor RV precision. The combination of the large collecting telescope area with the efficiency and the exquisite spectral fidelity of ESPRESSO opens a new parameter space in RV measurements, the study of planetary atmospheres, fundamental constants, stellar characterisation and many other fields., Comment: 26 pages, 28 figures

The bright star $\pi$ Men was chosen as the first target for a radial velocity follow-up to test the performance of ESPRESSO, the new high-resolution spectrograph at the ESO's Very-Large Telescope (VLT). The star hosts a multi-planet system (a transiting 4 M$_\oplus$ planet at $\sim$0.07 au, and a sub-stellar companion on a $\sim$2100-day eccentric orbit) which is particularly appealing for a precise multi-technique characterization. With the new ESPRESSO observations, that cover a time span of 200 days, we aim to improve the precision and accuracy of the planet parameters and search for additional low-mass companions. We also take advantage of new photometric transits of $\pi$ Men c observed by TESS over a time span that overlaps with that of the ESPRESSO follow-up campaign. We analyse the enlarged spectroscopic and photometric datasets and compare the results to those in the literature. We further characterize the system by means of absolute astrometry with Hipparcos and Gaia. We used the spectra of ESPRESSO for an independent determination of the stellar fundamental parameters. We present a precise characterization of the planetary system around $\pi$ Men. The ESPRESSO radial velocities alone (with typical uncertainty of 10 cm/s) allow for a precise retrieval of the Doppler signal induced by $\pi$ Men c. The residuals show an RMS of 1.2 m/s, and we can exclude companions with a minimum mass less than $\sim$2 M$_\oplus$ within the orbit of $\pi$ Men c). We improve the ephemeris of $\pi$ Men c using 18 additional TESS transits, and in combination with the astrometric measurements, we determine the inclination of the orbital plane of $\pi$ Men b with high precision ($i_{b}=45.8^{+1.4}_{-1.1}$ deg). This leads to the precise measurement of its absolute mass $m_{b}=14.1^{+0.5}_{-0.4}$ M$_{Jup}$, and shows that the planetary orbital planes are highly misaligned., Comment: Accepted for publication on A&A

We characterized the transiting planetary system orbiting the G2V star K2-38 using the new-generation echelle spectrograph ESPRESSO. We carried out a photometric analysis of the available K2 photometric light curve of this star to measure the radius of its two known planets. Using 43 ESPRESSO high-precision radial velocity measurements taken over the course of 8 months along with the 14 previously published HIRES RV measurements, we modeled the orbits of the two planets through a MCMC analysis, significantly improving their mass measurements. Using ESPRESSO spectra, we derived the stellar parameters, $T_{\rm eff}$=5731$\pm$66, $\log g$=4.38$\pm$0.11~dex, and $[Fe/H]$=0.26$\pm$0.05~dex, and thus the mass and radius of K2-38, $M_{\star}$=1.03 $^{+0.04}_{-0.02}$~M$_{\oplus}$ and $R_{\star}$=1.06 $^{+0.09}_{-0.06}$~R$_{\oplus}$. We determine new values for the planetary properties of both planets. We characterize K2-38b as a super-Earth with $R_{\rm P}$=1.54$\pm$0.14~R$_{\rm \oplus}$ and $M_{\rm p}$=7.3$^{+1.1}_{-1.0}$~M$_{\oplus}$, and K2-38c as a sub-Neptune with $R_{\rm P}$=2.29$\pm$0.26~R$_{\rm \oplus}$ and $M_{\rm p}$=8.3$^{+1.3}_{-1.3}$~M$_{\oplus}$. We derived a mean density of $\rho_{\rm p}$=11.0$^{+4.1}_{-2.8}$~g cm$^{-3}$ for K2-38b and $\rho_{\rm p}$=3.8$^{+1.8}_{-1.1}$~g~cm$^{-3}$ for K2-38c, confirming K2-38b as one of the densest planets known to date. The best description for the composition of K2-38b comes from an iron-rich Mercury-like model, while K2-38c is better described by a rocky model with a H2 envelope. The maximum collision stripping boundary shows how giant impacts could be the cause for the high density of K2-38b. The irradiation received by each planet places them on opposite sides of the radius valley. We find evidence of a long-period signal in the radial velocity time-series whose origin could be linked to a 0.25-3~M$_{\rm J}$ planet or stellar activity., Comment: 16 pages, 14 figures

A \emph{$k$--bisection} of a bridgeless cubic graph $G$ is a $2$--colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes have order at most $k$. Ban and Linial conjectured that {\em every bridgeless cubic graph admits a $2$--bisection except for the Petersen graph}. In this note, we prove Ban--Linial's conjecture for claw--free cubic graphs.

The first generation of E-ELT instruments will include an optical-infrared High Resolution Spectrograph, conventionally indicated as EELT-HIRES, which will be capable of providing unique breakthroughs in the fields of exoplanets, star and planet formation, physics and evolution of stars and galaxies, cosmology and fundamental physics. A 2-year long phase A study for EELT-HIRES has just started and will be performed by a consortium composed of institutes and organisations from Brazil, Chile, Denmark, France, Germany, Italy, Poland, Portugal, Spain, Sweden, Switzerland and United Kingdom. In this paper we describe the science goals and the preliminary technical concept for EELT-HIRES which will be developed during the phase A, as well as its planned development and consortium organisation during the study., Comment: 12 pages, in Ground-based and Airborne Instrumentation for Astronomy VI, 2016, Proc. SPIE 9908, 23

The discovery of almost 2000 exoplanets has revealed an unexpectedly diverse planet population. Observations to date have shown that our Solar System is certainly not representative of the general population of planets in our Milky Way. The key science questions that urgently need addressing are therefore: What are exoplanets made of? Why are planets as they are? What causes the exceptional diversity observed as compared to the Solar System? EChO (Exoplanet Characterisation Observatory) has been designed as a dedicated survey mission for transit and eclipse spectroscopy capable of observing a large and diverse planet sample within its four-year mission lifetime. EChO can target the atmospheres of super-Earths, Neptune-like, and Jupiter-like planets, in the very hot to temperate zones (planet temperatures of 300K-3000K) of F to M-type host stars. Over the next ten years, several new ground- and space-based transit surveys will come on-line (e.g. NGTS, CHEOPS, TESS, PLATO), which will specifically focus on finding bright, nearby systems. The current rapid rate of discovery would allow the target list to be further optimised in the years prior to EChO's launch and enable the atmospheric characterisation of hundreds of planets. Placing the satellite at L2 provides a cold and stable thermal environment, as well as a large field of regard to allow efficient time-critical observation of targets randomly distributed over the sky. A 1m class telescope is sufficiently large to achieve the necessary spectro-photometric precision. The spectral coverage (0.5-11 micron, goal 16 micron) and SNR to be achieved by EChO, thanks to its high stability and dedicated design, would enable a very accurate measurement of the atmospheric composition and structure of hundreds of exoplanets., Comment: 50 pages, 30 figures. Experimental Astronomy

In this note we construct a new infinite family of $(q-1)$-regular graphs of girth $8$ and order $2q(q-1)^2$ for all prime powers $q\ge 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself., Comment: 8 pages, 2 figures

Let $q\ge 2$ be a prime power. In this note we present a formulation for obtaining the known $(q+1,8)$-cages which has allowed us to construct small $(k,g)$--graphs for $k=q-1, q$ and $g=7,8$. Furthermore, we also obtain smaller $(q,8)$-graphs for even prime power $q$., Comment: 14 pages, 2 figures

A graph $G$ is $1$-extendible if every edge belongs to at least one $1$-factor of $G$. Let $G$ be a graph with a $1$-factor $F$. Then an even $F$-orientation of $G$ is an orientation in which each $F$-alternating cycle has exactly an even number of edges directed in the same fixed direction around the cycle. In this paper, we examine the structure of 1-extendible graphs $G$ which have no even $F$-orientation where $F$ is a fixed $1$-factor of $G$. In the case of graphs of connectivity at least four and k-regular graphs for $k \geq 3$ we give a complete characterization., Comment: 31 pages, 9 figures

The acronym ESPRESSO stems for Echelle SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observations; this instrument will be the next VLT high resolution spectrograph. The spectrograph will be installed at the Combined-Coud\'e Laboratory of the VLT and linked to the four 8.2 m Unit Telescopes (UT) through four optical Coud\'e trains. ESPRESSO will combine efficiency and extreme spectroscopic precision. ESPRESSO is foreseen to achieve a gain of two magnitudes with respect to its predecessor HARPS, and to improve the instrumental radial-velocity precision to reach the 10 cm/s level. It can be operated either with a single UT or with up to four UTs, enabling an additional gain in the latter mode. The incoherent combination of four telescopes and the extreme precision requirements called for many innovative design solutions while ensuring the technical heritage of the successful HARPS experience. ESPRESSO will allow to explore new frontiers in most domains of astrophysics that require precision and sensitivity. The main scientific drivers are the search and characterization of rocky exoplanets in the habitable zone of quiet, nearby G to M-dwarfs and the analysis of the variability of fundamental physical constants. The project passed the final design review in May 2013 and entered the manufacturing phase. ESPRESSO will be installed at the Paranal Observatory in 2016 and its operation is planned to start by the end of the same year., Comment: 12 pages, figures included, accepted for publication in Astron. Nachr

The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$--cages have been obtained from the projective planes of order $q$. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on $\mathbb{F}_q$. In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the $(q+1,8)$--cages arising from the generalized quadrangles of order $q$, $q$ a prime power.

Let $2 \le r < m$ and $g$ be positive integers. An $({r,m};g)$--graph} (or biregular graph) is a graph with degree set ${r,m}$ and girth $g$, and an $({r,m};g)$-cage (or biregular cage) is an $({r,m};g)$-graph of minimum order $n({r,m};g)$. If $m=r+1$, an $({r,m};g)$-cage is said to be a semiregular cage. In this paper we generalize the reduction and graph amalgam operations from M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate (2011) on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are $({r,2r-3};5)$-cages for all $r=q+1$ with $q$ a prime power, and $({r,2r-5};5)$-cages for all $r=q+1$ with $q$ a prime. The new semiregular cages are constructed for r=5 and 6 with 31 and 43 vertices respectively.

A {\em snark} is a cubic cyclically 4-edge connected graph with edge chromatic number four and girth at least five. We say that a graph $G$ is {\em odd 2-factored} if for each 2-factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2--factored snarks. In particular, we construct two families of odd 2-factored snarks that disprove a conjecture by some of the authors. Moreover, we approach the problem of characterizing odd 2-factored snarks furnishing a partial characterization of cyclically 4-edge connected odd 2-factored snarks. Finally, we pose a new conjecture regarding odd 2-factored snarks.

MOONS is a new conceptual design for a Multi-Object Optical and Near-infrared Spectrograph for the Very Large Telescope (VLT), selected by ESO for a Phase A study. The baseline design consists of 1000 fibers deployable over a field of view of 500 square arcmin, the largest patrol field offered by the Nasmyth focus at the VLT. The total wavelength coverage is 0.8um-1.8um and two resolution modes: medium resolution and high resolution. In the medium resolution mode (R=4,000-6,000) the entire wavelength range 0.8um-1.8um is observed simultaneously, while the high resolution mode covers simultaneously three selected spectral regions: one around the CaII triplet (at R=8,000) to measure radial velocities, and two regions at R=20,000 one in the J-band and one in the H-band, for detailed measurements of chemical abundances. The grasp of the 8.2m Very Large Telescope (VLT) combined with the large multiplex and wavelength coverage of MOONS - extending into the near-IR - will provide the observational power necessary to study galaxy formation and evolution over the entire history of the Universe, from our Milky Way, through the redshift desert and up to the epoch of re-ionization at z>8-9. At the same time, the high spectral resolution mode will allow astronomers to study chemical abundances of stars in our Galaxy, in particular in the highly obscured regions of the Bulge, and provide the necessary follow-up of the Gaia mission. Such characteristics and versatility make MOONS the long-awaited workhorse near-IR MOS for the VLT, which will perfectly complement optical spectroscopy performed by FLAMES and VIMOS., Comment: 9 pages, 5 figures. To appear in the proceedings of the SPIE Astronomical Instrumentation + Telescopes conference, Amsterdam, 2012

Let $q$ be a prime power; $(q+1,8)$-cages have been constructed as incidence graphs of a non-degenerate quadric surface in projective 4-space $P(4, q)$. The first contribution of this paper is a construction of these graphs in an alternative way by means of an explicit formula using graphical terminology. Furthermore by removing some specific perfect dominating sets from a $(q+1,8)$-cage we derive $k$-regular graphs of girth 8 for $k= q-1$ and $k=q$, having the smallest number of vertices known so far.

In this paper we obtain $(q+3)$--regular graphs of girth 5 with fewer vertices than previously known ones for $q=13,17,19$ and for any prime $q \ge 23$ performing operations of reductions and amalgams on the Levi graph $B_q$ of an elliptic semiplane of type ${\cal C}$. We also obtain a 13-regular graph of girth 5 on 236 vertices from $B_{11}$ using the same technique.