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Given a finite group $G$, the commuting graph of $G$ is the simple graph whose vertex set is $G$, and two distinct vertices are adjacent if they commute. In this paper, we classify all finite groups whose commuting graph is split and threshold. We also investigate the structure of a group whose commuting graph is either a cograph or a chordal graph, and determine all non-abelian finite simple groups whose commuting graph is a cograph. The results partly answer a question by Peter J. Cameron established in 2022 in his survey paper on graphs defined on groups., 26 pages

The enhanced power graph of a finite group $G$, denoted by $\mathcal{P}_E(G)$, is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of $\mathcal{P}_E(G)$ are equal. Also, we classify all groups whose (proper) enhanced power graphs are strongly regular. Further, the vertex connectivity of the enhanced power graphs associated to some nilpotent groups is obtained. Finally, we obtain a lower bound and an upper bound for the Wiener index of $\mathcal{P}_E(G)$, where $G$ is a nilpotent group. The finite nilpotent groups attaining these bounds are also characterized., arXiv admin note: text overlap with arXiv:2207.04641

Let $ G $ be a finite group. The reduced power graph of $ G $ is the undirected graph whose vertex set consists of all elements of $ G $, and two distinct vertices $ x $ and $ y $ are adjacent if either $ \langle x\rangle \subset \langle y\rangle $ or $ \langle y\rangle \subset \langle x\rangle $. In this paper, we show that the reduced power graph of $ G $ is perfect and characterize all finite groups whose reduced power graphs are split graphs, cographs, chordal graphs, and threshold graphs. We also give complete classifications in the case of abelian groups, dihedral groups, and generalized quaternion groups.

A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. Let $A$ be a finite abelian group and $T$ a square-free subset of $A$. The Cayley sum graph of $A$ with respect to the connection set $T$ is a simple graph with $A$ as its vertex set, and two vertices $x$ and $y$ are adjacent whenever $x+y\in T$. A subgroup of $A$ is said to be a subgroup perfect code of $A$ if the subgroup is a perfect code of some Cayley sum graph of $A$. In this paper, we give some necessary and sufficient conditions for a subset of $A$ to be a perfect code of a given Cayley sum graph of $A$. We also characterize all subgroup perfect codes of $A$., Comment: 13 pp

A subset $C$ of the vertex set of a graph $\Gamma$ is called a perfect code of $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$. In this paper, we classify all connected quintic Cayley graphs on abelian groups that admit a perfect code, and determine completely all perfect codes of such graphs.

We determine the diameter of every connected component of the complement of the power graph and the enhanced power graph of a finite group, which completely answers two questions by Peter J. Cameron., 12 pages

Soil carbon isotopes (δ13C) provide reliable insights at a long-term scale for studying soil carbon turnover. The Tibetan Plateau (TP), called “the third pole of the earth” is one of the most sensitive areas to global climate change and exhibits an early warning signal of global warming. Although many studies detected the variability of soil δ13C at site scales, a knowledge gap still exists in the spatial pattern of topsoil δ13C across the TP. To fill the substantial knowledge gap, we first compiled a database of topsoil δ13C with 396 observations from published literatures. Then we applied a Random Forest (RF) algorithm – a machine learning approach, to predict the spatial pattern of topsoil δ13C and β (indicating the decomposition rate of soil organic carbon (SOC), calculated by δ13C divided by logarithmically converted SOC). Finally, two datasets – topsoil δ13C and β with a fine spatial resolution of 1 km across the TP were developed. Results showed that topsoil δ13C varied significantly among different ecosystem types (p < 0.001). Topsoil δ13C was −26.3 ± 1.60 ‰ (mean ± standard deviation) for forests, 24.3 ± 2.00 ‰ for shrublands, −23.9 ± 1.84 ‰ for grasslands, −18.9 ± 2.37 ‰ for deserts, respectively. RF could well predict the spatial variability of topsoil δ13C with a model efficiency of 0.62 and root mean square error of 1.12 ‰, enabling to derive data-driven δ13C and β products. Data-driven topsoil δ13C varied from −28.26 ‰ to −16.95 ‰, with the highest topsoil δ13C in the north and northwest TP and the lowest δ13C in Southeast or South TP, indicating strong spatial variabilities in topsoil δ13C. Similarly, there were strong spatial variabilities in data-driven β, with the lowest β values at the east and middle TP, indicating a higher SOC turnover in the east and middle TP compared that of other regions in the TP. This study was the first attempt to develop a fine resolution product of topsoil δ13C and β across the TP, which could provide an independent data-driven benchmark for biogeochemical cycling models to study SOC turnover and terrestrial carbon-climate feedbacks over the TP under climate change. The data-driven δ13C and β datasets are public available at https://doi.org/10.6084/m9.figshare.16641292.v2 (Tang, 2021).

The enhanced power graph of a group is the simple graph whose vertex set is consisted of all elements of the group, and whose any pair of vertices are adjacent if they generate a cyclic subgroup. In this paper, we classify all finite groups whose enhanced power graphs are split and threshold. We also classify all finite nilpotent groups whose enhanced power graphs are chordal graphs and cographs. Finally, we give some families of non-nilpotent groups whose enhanced power graphs are chordal graphs and cographs. These results partly answer a question posed by Peter J. Cameron., Comment: 18 pages

Let $G$ be a finite group. The co-prime order graph of $G$ is the graph whose vertex set is $G$, and two distinct vertices $x,y$ are adjacent if gcd$(o(x),o(y))$ is either $1$ or a prime, where $o(x)$ and $o(y)$ are the orders of $x$ and $y$, respectively. In this paper, we characterize all finite groups whose co-prime order graphs are complete and classify all finite groups whose co-prime order graphs are planar. Also, we compute the vertex-connectivity of the co-prime order graph of a cyclic group, a dihedral group and a generalized quaternion group, which answers a question by Banerjee (2019). Finally, we prove that, for a fixed positive integer $k$, there are finitely many finite groups whose co-prime order graphs have (non)orientable genus $k$. As applications, we classify all finite groups whose co-prime order graphs have (non)orientable genus one and two., There is an error in Sect. 4. We can not obtain the first main result of this section

The power graph Γ G of a finite group G is the graph whose vertex set is G , two distinct elements being adjacent if one is a power of the other. In this paper, we give sharp lower and upper bounds for the independence number of Γ G and characterize the groups achieving the bounds. Moreover, we determine the independence number of Γ G if G is cyclic, dihedral or generalized quaternion. Finally, we classify all finite groups G whose power graphs have independence number 3 or n − 2 , where n is the order of G .

The power graph of a finite group is the graph whose vertex set is the group, two distinct elements being adjacent if one is a power of the other. The enhanced power graph of a finite group is the graph whose vertex set consists of all elements of the group, in which two vertices are adjacent if they generate a cyclic subgroup. In this paper, we give a complete description of finite groups with enhanced power graphs admitting a perfect code. In addition, we describe all groups in the following two classes of finite groups: the class of groups with power graphs admitting a total perfect code, and the class of groups with enhanced power graphs admitting a total perfect code. Furthermore, we characterize several families of finite groups with power graphs admitting a perfect code, and several other families of finite groups with power graphs which do not admit perfect codes.

Graphs associated with groups and other algebraic structures have been actively investigated, since they have valuable applications in data mining. For a finite group G, let ΓG be the graph with the non-identity elements of G as the vertex set, and two vertices are adjacent if they respectively lie in two conjugate proper subgroups of G. ΓG is called the generalized power graph with respect to G. This paper explores how the graph theoretical properties of ΓG can affect on the group theoretical properties of G.

We give the characteristic polynomial of the distance or adjacency matrix of the strong power graph of a finite group, and compute its distance and adjacency spectrum., 6 pages

Let $G$ be a finite non-cyclic group. The non-cyclic graph $\Gamma_G$ of $G$ is the graph whose vertex set is $G\setminus Cyc(G)$, two distinct vertices being adjacent if they do not generate a cyclic subgroup, where $Cyc(G)=\{a\in G: \langle a,b\rangle\ \text{is cyclic for each } b\in G\}$. In this paper, we classify all finite non-cyclic groups $G$ such that $\Gamma_G$ has (non)orientable genus one., Comment: 9 pages, 3 figures

The power graph $\mathcal P_G$ of a finite group $G$ is the graph with the vertex set $G$, where two elements are adjacent if one is a power of the other. We first show that $\mathcal P_G$ has an transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups (under usual inclusion) to characterise the structure of $\mathcal P_G$. Finally, the closed formula for the metric dimension of $\mathcal P_G$ is established. As an application, we compute the metric dimension of the power graph of a cyclic group.

The phenology of a landscape is a key parameter in climate and biogeochemical cycle models and its correct representation is central to the accurate simulation of carbon, water and energy exchange between the land surface and the atmosphere. Whereas biogeographic phenological patterns and shifts have received much attention in temperate ecosystems, much less is known about the phenology of savannas, despite their sensitivity to climate change and their coverage of approximately one eighth of the global land surface. Savannas are complex assemblages of multiple tree, shrub, and grass vegetation strata, each with variable phenological responses to seasonal climate and environmental variables. The objectives of this study were to investigate biogeographical and inter-annual patterns in savanna phenology along a 1100. km ecological rainfall gradient, known as North Australian Tropical Transect (NATT), encompassing humid coastal Eucalyptus forests and woodlands to xeric inland Acacia woodlands and shrublands. Key phenology transition dates (start, peak, end, and length of seasonal greening periods) were extracted from 13. years (2000-2012) of Moderate Resolution Imaging Spectroradiometer (MODIS) Enhanced Vegetation Index (EVI) data using Singular Spectrum Analysis (SSA).Two distinct biogeographical patterns in phenology were observed, controlled by different climate systems. The northern (mesic) portion of the transect, from 12°S, to around 17.7°S, was influenced by the Inter-Tropical Convergence Zone (ITCZ) seasonal monsoon climate system, resulting in strong latitudinal shifts in phenology patterns, primarily associated with the functional response of the C4 grass layer. Both the start and end of the greening (enhanced vegetation activity) season occurred earlier in the northern tropical savannas and were progressively delayed towards the southern limit of the Eucalyptus-dominated savannas resulting in relatively stable length of greening periods. In contrast, the southern xeric portion of the study area was largely decoupled from monsoonal influences and exhibited highly variable phenology that was largely rainfall pulse driven. The seasonal greening periods were generally shorter but fluctuated widely from no detectable greening during extended drought periods to length of greening seasons that exceeded those in the more mesic northern savannas in some wet years. This was in part due to more extreme rainfall variability, as well as a C3/C4 grass-forb understory that provided the potential for extended greening periods. Phenology of Acacia dominated savannas displayed a much greater overall responsiveness to hydroclimatic variability. The variance in annual precipitation alone could explain 80% of the variances in the length of greening season across the major vegetation groups. We also found that increased variation in the timing of phenology was coupled with a decreasing tree-grass ratio. We further compared the satellite-based phenology results with tower-derived measures of Gross Ecosystem Production (GEP) fluxes at three sites over two contrasting savanna classes. We found good convergence between MODIS EVI and tower GEP, thereby confirming the potential to link these two independent data sources to better understand savanna ecosystem functioning. © 2013 Elsevier Inc.

Let G be a finite group, p the smallest prime dividing the order of G and P a Sylow p-subgroup of G with the smallest generator number d. We consider such a set Md(P) = {P1, P2, . . . , Pd} of maximal subgroups of P such that ∩di=1Pi = Φ(P). Groups with certain s-permutably embedded and weakly c-normal subgroups of prime power order are studied. We present some sufficient conditions for a group to be p-nilpotent or p-supersolvable.

© 2014 Elsevier Inc. Accurate estimation of carbon fluxes across space and time is of great importance for quantifying global carbon balances. Current production efficiency models for calculation of gross primary production (GPP) depend on estimates of light-use-efficiency (LUE) obtained from look-up tables based on biome type and coarse-resolution meteorological inputs that can introduce uncertainties. Plant function is especially difficult to parameterize in the savanna biome due to the presence of varying mixtures of multiple plant functional types (PFTs)with distinct phenologies and responses to environmental factors. The objective of this study was to find a simple and robust method to accurately up-scale savanna GPP fromlocal, eddy covariance (EC) flux tower GPP measures to regional scales utilizing entirely remote sensing oservations. Here we assessed seasonal patterns of Moderate Resolution Imaging Spectroradiometer (MODIS) vegetation productswith seasonal EC tower GPP (GPPEC) at four sites along an ecological rainfall gradient (the North Australian Tropical Transect, NATT) encompassing tropical wet to dry savannas. The enhanced vegetation index (EVI) tracked the seasonal variations of GPPEC well at both site- and cross-site levels (R2= 0.84). The EVI relationship with GPPEC was further strengthened through coupling with ecosystem light-use-efficiency (eLUE), defined as the ratio of GPP to photosynthetically active radiation (PAR). Two savanna landscape eLUEmodels, driven by top-of-canopy incident PAR (PARTOC) or top-of-atmosphere incident PAR (PARTOA) were parameterized and investigated. GPP predicted using the eLUE models correlated well with GPPEC, with R2 of 0.85 (RMSE = 0.76 g C m-2 d-1) and 0.88 (RMSE = 0.70 g C m-2 d-1) for PARTOC and PARTOA, respectively, and were significantly improved compared to the MOD17 GPP product (R2 = 0.58, RMSE= 1.43 g C m-2 d-1). The eLUE model also minimized the seasonal hysteresis observed between greenup and brown-down in GPPEC and MODIS satellite product relationships, resulting in a consistent estimation of GPP across phenophases. The eLUE model effectively integrated the effects of variations in canopy photosynthetic capacity and environmental stress on photosynthesis, thus simplifying the up-scaling of carbon fluxes from tower to regional scale. The results fromthis study demonstrated that region-wide savanna GPP can be accurately estimated entirely with remote sensing observations without dependency on coarse-resolution ground meteorology or estimation of light-use-efficiency parameters.

13 Pág. Departamento de Medio Ambiente y Agronomía​ (INIA), Remote sensing capabilities to monitor evergreen broadleaved vegetation are limited by the low temporal variability in the greenness signal. With canopy greenness computed from digital repeat photography (PhenoCam), we investigated how canopy greenness related to seasonal changes in leaf age and traits as well as variation of trees’ water fluxes (characterized by sap flow and canopy conductance). The results showed that sprouting leaves are mainly responsible for the rapid increase in canopy green chromatic coordinate (GCC) in spring. We found statistically significantly differences in leaf traits and spectral properties among leaves of different leaf ages. Specifically, mean GCC of young leaves was 0.385 ± 0.010 (mean ± SD), while for mature and old leaves was 0.369 ± 0.003, and 0.376 ± 0.004, respectively. Thus, the temporal dynamics of canopy GCC can be explained by changes in leaf spectral properties and leaf age. Sap flow and canopy conductance are both well explained by a combination of environmental drivers and greenness (96% and 87% of the variance explained, respectively). In particular, air temperature and vapor pressure deficit (VPD) explained most of sap flow and canopy conductance variance, respectively. Besides, GCC is an important explanatory variable for variation of canopy conductance may because GCC can represent the leaf ontogeny information. We conclude that PhenoCam GCC can be used to identify the leaf flushing for evergreen broadleaved trees, which carries important information about leaf ontogeny and traits. Thus, it can be helpful for better estimating canopy conductance which constraints water fluxes., The authors acknowledge the Alexander von Humboldt Foundation for supporting this research with the Max Planck Prize to Markus Reichstein. Yunpeng Luo and Mirco Migliavacca gratefully acknowledge the financial support from the China Scholarship Council. ADR acknowledges support for the PhenoCam network from the National Science Foundation ( DEB- 1702697 ). Javier Pacheco-Labrador and Mirco Migliavacca acknowledge the German Aerospace Center (DLR) project OBEF-Accross2 “The Potential of Earth Observations to Capture Patterns of Biodiversity” (Contract No. 50EE1912). The research also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 721995 and Ministerio de Economíay Competitividad through FLUXPEC CGL2012-34383 and SynerTGE CGL2015-G9095-R (MINECO/FEDER, UE) projects.

Australia experienced one of the worst droughts in history during the early 21st-century (termed the ‘big dry’), exerting negative impacts on food production and water supply, with increased forest die-back and bushfires across large areas. Following the ‘big dry’, one of the largest La Niña events in the past century, in conjunction with an extreme positive excursion of the Southern Annular Mode (SAM), resulted in dramatic increased precipitation from 2010 to 2011 (termed the ‘big wet’), causing widespread flooding and a recorded sea level drop. Despite these extreme hydroclimatic impacts, the spatial partitioning and temporal evolution of total water storage across Australia remains unknown. In this study we investigated the spatial-temporal impacts of the recent ‘big dry’ and ‘big wet’ events on Australia's water storage dynamics using the total water storage anomaly (TWSA) data derived from the Gravity Recovery and Climate Experiment (GRACE) satellites. Results showed widespread, continental-scale decreases in TWS during the ‘big dry’, resulting in a net loss of 3.89 ± 0.47 cm (299 km3) total water, while the ‘big wet’ induced a sharp increase in TWS, equivalent to 11.68 ± 0.52 cm (898 km3) of water, or three times the total water loss during the ‘big dry’. We found highly variable continental patterns in water resources, involving differences in the direction, magnitude, and duration of TWS responses to drought and wet periods. These responses clustered into three distinct geographic zones that correlated well with the influences from multiple large-scale climate modes. Specifically, a persistent increasing trend in TWS was recorded over northern and northeastern Australia, where the climate is strongly influenced by El Niño-Southern Oscillation (ENSO). By contrast, western Australia, a region predominantly controlled by the Indian Ocean Dipole (IOD), exhibited a continuous decline in TWS during the ‘big dry’ and only a subtle increase during the ‘big wet’, indicating a weak recovery of water storage. Southeastern Australia, influenced by combined ENSO, IOD and SAM interactions, exhibited a pronounced TWS drying trend during the ‘big dry’ followed by rapid TWS increases during the ‘big wet’, with complete water storage recoveries. A spatial intensification of the water cycle was further identified, with a wetting trend over wetter regions (northern and northeastern Australia) and a drying trend over drier regions (western Australia). Our results highlight the value of GRACE derived TWSA as an important indicator of hydrological system performance for improved water impact assessments and management of water resources across space and time. Refereed/Peer-reviewed