Grundy domination and zero forcing in Kneser graphs

In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs Kn,r. In particular, we establish that the Grundy total domination number γ t gr(Kn,r) equals 2r r for any r ≥ 2 and n ≥ 2r + 1. For the Grundy domination number of Kneser graphs we get γgr(Kn,r) = α(Kn,r) whenever n is sufficiently larger than r. On the other hand, the zero forcing number Z(Kn,r) is proved to be n r − 2r r when n ≥ 3r + 1 and r ≥ 2, while lower and upper bounds are provided for Z(Kn,r) when 2r + 1 ≤ n ≤ 3r. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way.Fil: Bresar, Bostjan. University of Maribor; Eslovenia. Institute Of Mathematics, Physics And Mechanics Ljubljana; EsloveniaFil: Kos, Tim. Institute Of Mathematics, Physics And Mechanics Ljubljana; EsloveniaFil: Torres, Pablo Daniel. Universidad Nacional de Rosario. Facultad de Ciencias Exactas Ingeniería y Agrimensura. Escuela de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentin

Complete Tidal Evolution of Pluto-Charon

Both Pluto and its satellite Charon have rotation rates synchronous with their orbital mean motion. This is the theoretical end point of tidal evolution where transfer of angular momentum has ceased. Here we follow Pluto's tidal evolution from an initial state having the current total angular momentum of the system but with Charon in an eccentric orbit with semimajor axis $a \approx 4R_P$ (where $R_P$ is the radius of Pluto), consistent with its impact origin. Two tidal models are used, where the tidal dissipation function $Q \propto$ 1/frequency and $Q=$ constant, where details of the evolution are strongly model dependent. The inclusion of the gravitational harmonic coefficient $C_{22}$ of both bodies in the analysis allows smooth, self consistent evolution to the dual synchronous state, whereas its omission frustrates successful evolution in some cases. The zonal harmonic $J_2$ can also be included, but does not cause a significant effect on the overall evolution. The ratio of dissipation in Charon to that in Pluto controls the behavior of the orbital eccentricity, where a judicious choice leads to a nearly constant eccentricity until the final approach to dual synchronous rotation. The tidal models are complete in the sense that every nuance of tidal evolution is realized while conserving total angular momentum - including temporary capture into spin-orbit resonances as Charon's spin decreases and damped librations about the same.Comment: 36 pages, including 18 figures; accepted for publication in Icaru

Indicated total domination game

A vertex $u$ in a graph $G$ totally dominates a vertex $v$ if $u$ is adjacent to $v$ in $G$. A total dominating set of $G$ is a set $S$ of vertices of $G$ such that every vertex of $G$ is totally dominated by a vertex in $S$. The indicated total domination game is played on a graph $G$ by two players, Dominator and Staller, who take turns making a move. In each of his moves, Dominator indicates a vertex $v$ of the graph that has not been totally dominated in the previous moves, and Staller chooses (or selects) any vertex adjacent to $v$ that has not yet been played, and adds it to a set $D$ that is being built during the game. The game ends when every vertex is totally dominated, that is, when $D$ is a total dominating set of $G$. The goal of Dominator is to minimize the size of $D$, while Staller wants just the opposite. Providing that both players are playing optimally with respect to their goals, the size of the resulting set $D$ is the indicated total domination number of $G$, denoted by $\gamma_t^{\rm i}(G)$. In this paper we present several results on indicated total domination game. Among other results we prove the Indicated Total Continuation Principle, and we show that the indicated total domination number of a graph is bounded below by the well studied upper total domination number.Comment: 20 pages, 6 figures, 18 references, corrected a reference and added MSC clas

Correspondence of butterfly and host plant diversity: Foundation for habitat restoration and conservation

At a spatial scale, the diversity of butterflies varies with numerous factors including the availability of the host plant species. In parity with this proposition, the correspondence of diversity of butterfly and plant in the background of the urban–rural gradient was evaluated using Kolkata, India, as a model study area. The results reveal significant positive correlation between the diversity of butterflies and the plants, with the different values for the suburban, rural, and urban areas. Identification of the butterfly loads for the plants in the respective areas can be useful in enhancing the conservation of the butterflies through enhanced plantation of the concerned plant species. Alternatively, the disclosure of the generalist and specialist pattern of the plant species preference by the butterflies may be useful in enhancing the population of the respective species in the concerned areas. The conservation strategy for butterfly species may be refined through the use of both or any one of the quantitative assessment of the butterfly–plant links in the urban–rural gradient in Kolkata, India, and similar places in the world

Muscle p70S6K phosphorylation in response to soy and dairy rich meals in middle aged men with metabolic syndrome: a randomised crossover trial

The mammalian target of rapamycin (mTOR) pathway is the primary regulator of muscle protein synthesis. Metabolic syndrome (MetS) is characterized by central obesity and insulin resistance; little is known about how MetS affects the sensitivity of the mTOR pathway to feeding

Pedigree analysis applied to an endangered buffalo population: possible management strategy.

The Carabao breed (Bubalus bubalis kerebao) in Brazil may be endangered and at risk of losing specific qualities. This makes preservation and population studies extremely important. In this pedigree analysis on a Brazilian herd, low values for populational parameters and high mean endogamy were found. Mating optimization based on bulls of lesser kinship improves populational parameters and reduces inbreeding rates. Use of this tool, in addition to conservation programs, will help to mitigate genetic variability losses in the Brazilian Carabao herd, thus allowing its future enrollment in genetic improvement programs