Double Stars Research Articles

Chordal Graphs, Even‐Hole‐Free Graphs and Sparse Obstructions to Bounded Treewidth

ABSTRACTEven‐hole‐free graphs pose a central challenge in identifying hereditary classes of bounded treewidth. We investigate this matter by presenting and studying the following conjecture: for an integer and a graph , every even‐hole‐free graph of large enough treewidth has an induced subgraph isomorphic to either or , if (and only if) is a ‐free chordal graph. The “only if” part follows from the properties of the so‐called layered wheels, a construction by Sintiari and Trotignon consisting of (even‐hole, )‐free graphs with arbitrarily large treewidth. Alecu et al. proved recently that the conjecture holds in two special cases: (a) when ; and (b) when for some forest ; that is, is obtained from a forest by adding a universal vertex. Our first result is a common strengthening of (a) and (b): for an integer and graphs and , (even‐hole, )‐free graphs have bounded treewidth if and only if is a forest and is a ‐free chordal graph. Also, for general , we push the current state of the art further than (b) by settling the conjecture for the smallest choices of that are not coned forests. The latter follows from our second result: we prove the conjecture when is a crystal; that is, a graph obtained from arbitrarily many coned double stars by gluing them together along the “middle” edges of the double stars. In the first version of this paper, we suggested the following which is a strengthening of our main conjecture: for every , every graph of sufficiently large treewidth has an induced subgraph of treewidth which is either complete, complete bipartite, or 2‐degenerate. This strengthening has now been refuted by Chudnovsky and Trotignon [On treewidth and maximum cliques, arxiv:2405.07471, 2024].

Atom bond connectivity index for graph with self-loops and its application to structure property relationships in anticancer drugs

Let be a graph derived from a simple graph G by adding a self-loop to each vertex in a subset . In this paper, we define the atom bond connectivity index of the graph as and the atom bond connectivity energy of as . We obtained upper bounds for the ABC spectral radius of the graph as well as bounds for and in terms of m, n, and . Additionally, we computed the ABC energy for complete graph, cocktail party graph and crown graph with self-loops. We also derived the characteristic polynomial of double star graph with self-loops. Furthermore, we explored the correlation between and various physico-chemical properties, such as boiling point (BP) and molar refraction (MR). Furthermore, we established correlations between and specific indices, specifically the Sombor index of a graph , first Zagreb index of a graph , and Randic index of a graph .

Analyzing Restrained Pitchfork Domination Across Path-Related Graph Structures

Let G = (V,E) be a finite, simple, and undirected graph without an isolated vertex. A dominating subset D ⊆ V (G) is a restrained pitchfork dominating set if 1 ≤ |N(u) ∩ V − D| ≤ 2 for every u ∈ D and every vertex not in D is adjacent to at least one vertex in the same set. The cardinality of a minimum restrained pitchfork dominating set is the restrained pitchfork domination number γrpf(G). In the course of this investigation, we undertake an examination of the restrained pitchfork domination number within various path-related graphs. This analysis encompasses a range of graph structures, including the coconut tree, double star, banana tree, binomial tree, thorn path, thorn graph, and the square of the path denoted as Pn.

Uncertainties in Ground‐Based Visual Double Star Measures—II Accuracy of Measures

ABSTRACTLetchford and White 2025, Paper I, determined the uncertainties in ground‐based historic measures of double stars. In this paper, the accuracy of 26,205 ground‐based measures of 857 visual double stars, made since 1780, is determined relative to space‐based measures based on positions and proper motion from the HIPPARCOS (via ASCC) and Gaia DR3 missions. We determine the accuracy of measures for the epoch of observation, the size of the telescope, the different attached instruments, and the filter applied. We find that the accuracy of the measures is improving with time; however, the typical telescope used for double‐star observations has been, and continues to be, relatively small. Modern instrumentation such as speckle interferometry and lucky imaging has advanced the accuracy by a factor of ten over traditional micrometre measurements.

Topological aspects of double neutron star formation: Its application to the gravitational-wave signatures

Topology is important in understanding the merger process of Double neutron stars (DNSs). NSs result from evolution of massive stars, giving rise to the formation of two closely orbiting neutron stars. Detecting the source of gravitational waves from DNSs represents the endpoint of binary stellar evolution. This paper explores the exciting relationship between topology, geometry, and astrophysics, with a specific emphasis on dynamical formation and evolution of DNSs. Within this research, we investigate the topological and geometric properties of these systems in the context of connected sum and wedge sum spaces. Furthermore, we introduce the concept of folding and retraction within the framework of the connected sum of DNSs, elucidating the topological characteristics that emerge when two distinct neutron stars merge. This topological operation provides valuable insights into the stellar evolution of these binary systems. In addition, we can utilize the phenomenological waveform templates in spacetime for gravitational wave observations.

Analysis of Electrical Faults and Mitigation Strategies for Double-star Induction Machines

Double star electric machines are renowned for their robustness, reliability and torque quality. However, despite these advantages, they are prone to various mechanical and electrical faults. This research investigates the impact of electrical faults on double-star induction machines (DSIMs), encompassing phase-open and inter-turn short-circuit failures in both stator and rotor windings. A real abc framework is employed, considering both connected and unconnected neutral configurations, to accurately model the behavior of the machine under healthy and degraded conditions. Simulation results reveal that open-phase faults (OPF) lead to current imbalances, torque fluctuations, and speed variations, which can be mitigated through an intentional adjacent second-phase opening. Additionally inter-turn short-circuit faults (ITSCF) severity is found to be highly dependent on fault resistance, influencing current distortion and electromagnetic disturbances. The results demonstrate that the suitable configuration of the neutral depends on depends on the fault type: connecting the neutral (CN) generally reduces the severity of OPF issues, whereas disconnecting the neutral (UNC) is more effective for mitigating stator ITSCF. These strategies effectively reduce disturbances and minimize torque and speed ripples, thereby maintaining optimal machine performance. Furthermore, detailed spectral analysis of DSIM signatures is performed, highlighting the complexities involved in fault diagnosis and emphasizing the importance of accurate fault identification for ensuring system reliability. These findings offer valuable insights into fault-tolerant strategies and DSIM reliability enhancement. This guarantees service continuity while keeping the main loads connected.

Double star arrangement and the pointed multinet

Abstract Let be a hyperplane arrangement in a complex projective space. It is an open question if the degree one cohomology jump loci (with complex coefficients) are determined by the combinatorics of . By the work of Falk and Yuzvinsky [Compositio Math. 143 (2007), no. 4, 1069–1088] and Marco‐Buzunáriz [Graphs Combin. 25 (2009), no. 4, 469–488], all the irreducible components passing through the origin are determined by the multinet structure, which is combinatorially determined. Denham and Suciu introduced the pointed multinet structure, which is combinatorially determined, to obtain examples of arrangements with translated positive‐dimensional components in the degree one cohomology jump loci [Proc. Lond. Math. Soc. (3) 108 (2014), no. 6, 1435–1470]. Suciu asked the question if all translated positive‐dimensional components appear in this manner [Ann. Fac. Sci. Toulouse Math. (6) 23 (2014), no. 2, 417–481]. In this paper, we show that the double star arrangement introduced by Ishibashi, Sugawara, and Yoshinaga [Adv. in Appl. Math. 162 (2025), Paper No. 102790, Example 3.2] gives a negative answer to this question.

On the complexity of perfect Roman domination and perfect double Roman domination

For a graph [Formula: see text] and a function [Formula: see text], let [Formula: see text] ([Formula: see text]) be the set of vertices assigned the value [Formula: see text] by [Formula: see text]. A perfect Roman dominating function on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] is adjacent to exactly one vertex [Formula: see text]. A perfect double Roman dominating function of a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that (1) every vertex [Formula: see text] is adjacent to exactly two vertices in [Formula: see text] and no vertex in [Formula: see text], or exactly one vertex in [Formula: see text] and no vertex in [Formula: see text]; (2) If [Formula: see text], then [Formula: see text] is adjacent to exactly one vertex in [Formula: see text] and no vertex in [Formula: see text]. In this paper, we prove that the decision problem associated to perfect Roman domination problem is NP-complete even when restricted to double star convex bipartite graphs, and the decision problem associated to perfect double Roman domination problem is NP-complete for comb convex bipartite graphs. We also prove that the decision problem associated to a similar Roman domination variant, namely minimum independent Roman domination problem is NP-complete even when restricted to double star convex bipartite graphs.

Detection of Low‐Altitude Cislunar Dust With the Lunar Occultation Archive

Abstract It is believed that dust formations above the lunar surface, manifested via sunlight scattering and detected in‐situ, are of too low density to pose threats to lunar missions. However, occasionally prolonged fading/kindling of the immersing/emerging stars near the lunar limb indicates much denser low‐altitude dust clouds. We performed statistical analysis of such abnormal stellar occultation events (ASOEs), found in the Lunar Occultation Archive. Specific dependence of their duration on selenographic position reveals an impact‐plume like shape of dust clouds and excludes visual illusions, terrestrial cloudiness, and double stars as causes of the observed starlight extinction. The probability of the long‐lasting ASOEs peaks during the Perseid meteor shower in August, confirming the impact‐related nature of most of the related dust clouds. At the same time, additional semi‐monthly periodicity of ASOEs points to a complementary mechanism of dust lifting due to, for example, lunar outgassing triggered by solar tides.

Disentangling Joint Light Curves Using Photocenter Shifts: A Case Study Using NEOWISE Data

Abstract The data collected by the Wide-field Infrared Survey Explorer (WISE) and its follow-up Near Earth Object (NEO) mission (NEOWISE) represent a treasure trove for variability studies. However, the angular resolution imposed by the primary mirror implies that close double stars are often unresolved. Then, variability of one or both stars leads to motion of the image centroid along the connecting line. Knowledge of the angular separation, derived from higher-resolution imaging which resolves both components, allows disentangling of the joint light curve into individual ones. This is illustrated by the case of SPICY 1474 which featured an outburst several years ago. Removal of the contribution of the nearby companion, which led to a dilution of the burst strength, revealed that it was ∼0.5 mag brighter than in the joint light curve. A comparison with light curves from unTimely suggests that utilizing the photocenter shift may lead to more reliable results.

Kinematic solutions in the Washington Double Star catalog: adding 169,000 orbits to the Visual Orbit catalog

Kinematic solutions in the Washington Double Star catalog: adding 169,000 orbits to the Visual Orbit catalog

Resilient single-star and passive double-star fiber links for point-to-multipoint optical networks with switchable path protection

This study focuses on the design of a new, to the best of our knowledge, switchable network with disaster resilience in mind. Specifically, it introduces a redundant link configuration consisting of a single star (SS) type provided to each optical distribution terminal (ODT) as the primary link and a passive double star (PDS) type provided to all ODTs as the secondary link. This configuration allows for a point-to-multipoint (P-to-MP) optical network that can switch between SS and PDS links using an optical switch to achieve rapid recovery and improved reliability during disasters. The study meticulously compares the capital cost and availability of the SS configuration, the PDS configuration, and the SS/PDS switchable configuration with and without variable reflection blocking (VRB). In addition, a bidirectional transmission experiment was conducted using wavelength conversion with two light sources and VRB to address single-link failures. The experimental results unequivocally confirmed that the proposed configuration functions effectively during link failures, ensuring energy-efficient operation and superior capital cost efficiency. Furthermore, it was demonstrated that using VRB at the ODT side allows for bidirectional communication while effectively suppressing reflections, further enhancing the system’s capital and operation cost efficiency. The proposed P-to-MP optical network configuration effectively ensures redundancy and reliability while accommodating the expanded scale of optical fiber deployment in next-generation mobile communication systems.

The Neutron Star Merger Delay-time Distribution, R-process “Knees,” and the Metal Budget of the Galaxy

Abstract For a sample of 18 currently known recycled millisecond pulsars (rMSPs) that are in double neutron star (DNS) systems, and 42 rMSPs with similar properties that are not in DNS pairs, we analyze the distributions of the characteristic age, τ c , and the time-until-merger of the double systems, τ gw. Based on the τ c distribution of non-DNS rMSPs, we argue that τ c is a reasonable estimator of true pulsar age and that rMSPs are active as pulsars for a long (≳Hubble) time. Among the DNSs there is an excess of young systems (small τ c ) with short life expectancy (small τ gw) compared to model expectations for the distributions of τ c and τ gw if, at birth, DNSs have a delay-time distribution (DTD) of the form ∼ τ gw − 1 (expected generically for close binaries), or for that matter, from expectations from any single power-law DTD. A two-population DNS model solves the problem: the data are best fit by the combination of a “fast” population with DTD going as τ gw − 1.9 ± 0.4 , and a “slow” population of DNSs, with DTD proportional to τ gw − 1.1 ± 0.15 . The fast population can be equivalently represented by a shallow power-law DTD with an exponential cutoff beyond τ gw ∼ 300 Myr. The fast population completely dominates, by a factor A ≈ 10–100, the numbers of DNSs that merge within a Hubble time, and that presumably lead to short gamma-ray bursts and kilonova explosions. Using a simple, empirically based, chemical-evolution calculation, we show that the fast/steep kilonova DTD, convolved with the measured star formation history of the Milky Way’s thick-disk population, naturally reproduces the “knee” structure seen in abundance-ratio diagrams of thick-disk stars, for europium and for two other r-process elements. As a corollary, we show, based again solely on empirical input concerning iron production by supernovae, that the Milky Way is nearly a “closed box” that has retained at least ∼70%–90% of the metals produced over the Galaxy’s lifetime.

Various Labelling for Double Star Graph

In this work, we introduce labeling techniques for the double star graph, a basic graph theory structure. In particular, we concentrate on calculating two different kinds of labeling: fortunate labeling and correct labeling. Adhering to the restrictions of vertex labeling in graph theory, appropriate labeling guarantees that neighboring vertices receive unique labels. A more recent and interesting idea is the fortunate labelling, which gives vertices positive numbers so that the labels on neighboring vertices add up to a unique value for each edge. We calculate and examine various labeling methods using algorithmic methods, proving their usefulness and effectiveness for the double star graph. Our findings further enhance the theoretical and practical capabilities of various labeling systems by offering insightful information about how to optimize them for bipartite and tree-like graphs.

Graph Entropy Based on Wiener Polarity Index Under Four Kinds of Graph Operations

The Wiener polarity index of a graph <i>G</i>, is the number of unordered pairs of vertices that are at distance 3 in <i>G</i>. This index can reflect the specific distance relation between vertices in the graph, and provides a new way for the study of graph structure. In this paper, the graph entropy based on Wiener polarity index defined. Based on the above definition of graph entropy, it compares the graph entropy of path and balanced double star graphs based on Wiener polarity index. The expressions of graph entropy based on Wiener polarity index for trees with diameter <i>d ≥ 3</i> are studied under four graph operations: tensor product, strong product, Cartesian product and composite graph.

From Be X-Ray Binaries to Double Neutron Stars: Exploring the Spin and Orbital Evolution

We explore the evolutionary link between Galactic Be X-ray binaries (BeXBs) and Galactic field double neutron stars (DNSs) based on the properties of the NS spin period—P and binary orbital period—Porb. First, both BeXB and DNS sources show positive correlation trends in P versus Porb relation (P−Porb diagram), which may relate to the influence of the accretion evolution. Secondly, the two types of sources exhibit similar bi-modal P/Porb distributions with the gaps of P∼40 s/Porb∼60 days for BeXBs and P∼50 ms/Porb∼1 day for DNSs, respectively. We propose a possibility that Galactic BeXBs may transfer the bi-modal P/Porb classifications to Galactic field DNSs during the evolution process. Furthermore, based on the bi-modal gaps, we infer the contraction factors of P (by ∼1800) and Porb (by ∼160) valuesin the evolution from Galactic BeXBs to Galactic field DNSs. We find that the scaled P or Porb values of Galactic BeXBs share the similar bi-modal distributions to that of Galactic field DNSs, and these results can offer a reference to trace the classification and evolution between the two types of sources.

The Total Disjoint Irregularity Strength of a Double and Triple Star Graphs

The Total Disjoint Irregularity Strength of a Double and Triple Star Graphs

The Effect of Donor Star Rejuvenation on Common Envelope Evolution

Abstract In close binary star systems, common envelope evolution (CEE) may occur after a previous phase of mass transfer. Some isolated formation channels for double neutron star binaries suggest that the donor of CEE was the accretor of a previous phase of stable mass transfer. Accretion should substantially alter the structure of the donor, particularly by steepening the density gradient at the core-envelope interface and rejuvenating the star. We study the CEE of a donor that was the accretor of a previous phase of stable mass transfer and has a rejuvenated structure. We perform 3D hydrodynamics simulations of the CEE of an 18 M ⊙ supergiant with a 1.4 M ⊙ companion using rejuvenated and non-rejuvenated 1D stellar models for the donor. We compare the two simulations to characterize the effect of the rejuvenation on the outcome of the common envelope phase and the shape of the ejecta. We find that accounting for a previous phase of mass transfer reduces the duration of the inspiral phase by a factor of two, likely due to the different structures in the outer layers of the donor. In the rejuvenated case, the simulations show more equatorially concentrated and asymmetric ejecta, though both cases display evidence for the formation of a pressure-supported thick circumbinary disk. During the dynamical inspiral phase, the impact of rejuvenation on the unbinding of the envelope is unclear; we find that rejuvenation decreases the amount of unbound mass by 20%–40% depending on the energy criterion used.

Uncertainties in Ground‐Based Visual Double Star Measures

ABSTRACTStellar masses are found from the orbital elements of binary systems which are, in turn, computed from weighted astrometric measures. Astrometric measures of double stars (their position angle and separation) rarely include uncertainties, and published binary star orbits rarely include the weighting systems used in the determination of the orbital elements. Here we propose a simple method for estimating uncertainties of ground‐based measures of visual double stars based on precision space‐based astrometry of optical (not binary) double stars, which can be used as unbiased weights for all double star measures. The precision of ground‐based measures is examined as (i) a function of the date of observation, (ii) the telescope aperture, and (iii) the instrumentation (technique) used at the telescope. We also note in the Appendix, 19 pairs that are incorrectly described in Lin2 and six rectilinear pairs that may display curved motion.

On the Exponential Atom-Bond Connectivity Index of Graphs

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: eABC=eABC(Υ)=∑vivj∈E(Υ)edi+dj−2didj, where di is the degree of the vertex vi in Υ. In this paper, we prove that the double star DSn−3,1 is the second maximal graph with respect to the eABC index of trees of order n. We give an upper bound on eABC of unicyclic graphs of order n and characterize the maximal graphs. The graph K1∨(P3∪(n−4)K1) gives the maximal graph with respect to the eABC index of bicyclic graphs of order n. We present several relations between eABC(Υ) and ABC(Υ) of graph Υ. Finally, we provide a conclusion summarizing our findings and discuss potential directions for future research.