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In 1996, F & agrave;brega and Fiol introduced the g-extra connectivity of Gas an important parameter for the fault tolerance of an interconnection network. A subset of vertices S is said to be a cutset if G-S is not connected. A cutset S is called an Rg-cutset, where g is a non-negative integer, if every component of G-S has at least g + 1 vertices. If G has at least one Rg-cutset, the g-extra connectivity of G, denoted by kappa g(G), is then defined as the minimum cardinality over all Rg-cutsets of G. In this paper, we obtain the exact values of the g-extra connectivity of some special graph classes, and show that & LeftFloor; n-3 & RightFloor; 1 <= kappa g(G) <= n-2g-2 for 0 <= g <= 2 , and graphs with kappa g(G) = 1, 2, 3 and trees with kappa g(Tn) = n-2g-2 are characterized, respectively. We also derive three extremal results for the g-extra connectivity. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
The spectroscopy of the 3++ light-meson candidates, in particular the a3 and f3 families, remains an open issue. We compute the mass spectra in the modified Godfrey-Isgur model and evaluate the Okubo-Zweig-Iizuka-allowed two-body strong decays within the quark-pair-creation model. Our analysis favors the interpretation that a3(1875) and a3(2030) correspond to the same resonance, identified as the a3 ground state, while f3(2050) is the ground state of the f3 family; furthermore, a3(2275) and f3(2300) are assigned as their first radial excited states. For other higher-excitation states, we provide predictions for the decay behaviors and include the mass-induced model uncertainty.
Source samples misclassification is a key source for the uncertainty in the aeolian sediment source tracking models. Therefore, identifying sources of aeolian sand and their samples correct classification are necessary to decrease the uncertainty associated with source tracking’s models. This research aimed to introduce deep clustering (DC) as a type of deep learning (DL) models for classifying the source samples for aeolian sand in a region with severe wind erosion and active sand dunes impacting on the railroad networks in the Zhongzaohuo in the Qaidam Basin of Tibetan Plateau, Northwest China. In this research, 40 samples taken from four potential source regions, and then, 40 geochemical elements and elementary compositions were measured in each sample by X-ray fluorescence spectrometer. To classify source samples of aeolian landforms, eight DC models based on deep Autoencoder (DAE) (e.g., Autoencoder, DCN, DEC, IDEC, DipDECK, DipEncoder, DDC and N2D) was employed to classify source samples of aeolian sand in our study area. Then, stepwise discriminant function analysis (DFA) was applied to explore the accuracy of source samples classified correctly in different source classification schemes provided by DC models. The results of the DC models revealed that the accuracy of source samples were classified correctly ranges between 82.5 and 100 An important source for uncertainty in the sediment source tracing models is source samples misclassification. In this study, we introduced eight deep clustering models based on deep autoencoder for classifying source samples of sand in the Qaidam Basin of Tibetan Plateau, Northwest China. 100
In multiprocessor systems, fault diagnosis technology is a core mechanism for ensuring system reliability and efficient operation. This paper proposes a new diagnosability parameter (referred to as g-extra H-structure diagnosability) for structural faults that may occur in multiprocessor systems, based on the number of nodes within each component of the remaining part (i.e., the system after removing the faulty nodes). We use the graph G to represent a multiprocessor system. A graph G is said to be g-extra H-structure t-diagnosable if, for any two distinct g-extra H-structure fault sets S_1 and S_2 with |S_1|≤ t and |S_2|≤ t , the vertex sets V(S_1) and V(S_2) are distinguishable under a given diagnosis model. The g-extra H-structure diagnosability of G, denoted by t^g_s(G; H) , is the maximum value of t such that G is g-extra H-structure t-diagnosable. This parameter refers to the maximum number of g-extra H-structure sets that the system can precisely detect by itself. The relationship between this parameter and the original H-structure diagnosability is also presented. Additionally, under the PMC and MM* diagnostic models, we determine t_s^g(Q_n;K_1,1) and t_s^g(Q_n;C_4) for g∈{1,2,3} , and t_s^g(Q_n;K_1,2) for hypercube Q_n with g∈{1,2} .
This study evaluated the spatial distribution and drivers of soil organic carbon (SOC), microbial biomass carbon (MBC), readily oxidizable carbon (ROC), non-labile organic carbon (NLOC), and the carbon pool management index (CPMI) in the 0–40 cm soil layer across forest, shrubland, and grassland on the southern slope of the Qilian Mountains. Results showed that forest soils had the highest SOC and MBC, while grassland soils had the lowest. ROC was significantly higher in shrubland, and grasslands had a higher proportion of NLOC. Forest soils also exhibited higher carbon pool activity (A), carbon activity index (AI), and CPMI, whereas grasslands had significantly lower values. Correlation analysis revealed significant positive relationships between SOC, NLOC, and MBC with soil water content (SWC), total nitrogen (TN), available nitrogen (AN), available phosphorus (AP), and enzyme activities (alkaline phosphatase, PHO; β-glucosidase, BG). ROC and CPMI were mainly influenced by electrical conductivity (EC), SWC, TN, AN, and total phosphorus (TP). Redundancy analysis (RDA) explained 96.02
