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Solar-assisted catalytic ozonation is a low-consumption and high-efficiency strategy for removing low-concentration VOCs. The photothermal conversion capability and catalytic ozonation activity of the catalyst need to be improved with a low load of noble metals. In this work, we coloaded Au and Pd on CeO2 to enhance photo-assisted catalytic ozonation performance through their synergistic effect. X-ray photoelectron spectroscopy and temperature-programmed desorption experiments were performed to analyze the effects of Au and Pd. Results show that the synergy factor of full-spectrum light and ozone for PdOx–Au–CeO2 was 8.94, 1.11, and 1.28 times higher than those for Au–CeO2 and PdO2–CeO2, respectively. Au loading significantly enhanced light absorption and photothermal-conversion capability. The coloading of Au and PdOx increased surface Ce3+–OH2+ and reduced the difficulty of surface oxygen vacancy formation, thereby promoting ozone utilization for toluene degradation. This work proposed a method of efficiently utilizing solar energy for VOC control. [ABSTRACT FROM AUTHOR]

In 1989, Chartrand, Oellermann, Tian and Zou introduced the Steiner distance for graphs. This is a natural generalization of the classical graph distance concept. Let Γ be a connected graph of order at least 2, and S \ V (Γ) . Then, the minimum size among all the connected subgraphs whose vertex sets contain S is the Steiner distance d Γ (S) among the vertices of S. The Steiner k-eccentricity e k (v) of a vertex v of Γ is defined by e k (v) = max { d Γ (S) | S \ V (Γ) , | S | = k , a n d v ∈ S } , where n and k are two integers, with 2 ≤ k ≤ n , and the Steiner k-diameter of Γ is defined by sdiam k (Γ) = max { e k (v) | v ∈ V (Γ) } . In this paper, we present an algorithm to derive the Steiner distance of a graph; in addition, we obtain a relationship between the Steiner k-diameter of a graph and its line graph. We study various properties of the Steiner diameter through a combinatorial approach. Moreover, we characterize graph Γ when sdiam k (Γ) is given, and we determine sdiam k (Γ) for some special graphs. We also discuss some of the applications of Steiner diameter, including one in education networks. [ABSTRACT FROM AUTHOR]

We generalise an approach to deriving diagnosability results of various interconnection networks in terms of the popular g-good-neighbour and g-extra fault-tolerant models, as well as mainstream diagnostic models such as the PMC and the MM* models. As demonstrative examples, we show how to follow this constructive, and effective, process to derive the g-extra diagnosabilities of the hypercube, the (n , k) -star, and the arrangement graph. These results agree with those achieved individually, without duplicating structure independent technical details. Some of them come with a larger applicable range than those already known, and the result for the arrangement graph in terms of the MM* model is new. [ABSTRACT FROM AUTHOR]

Connectivity type measures form an important part of network analysis, in particular, in analyzing vulnerability and resiliency of interconnection networks. One such measure is to consider the structure of the resulting graph when "many" vertices are deleted. In this short note, we study a way to extend some known results on this topic. [ABSTRACT FROM AUTHOR]

Connectivity type measures form an important topic in graph theory. Such measures provide an important part of analyzing the vulnerability and resilience of interconnection networks. In this short commentary, we outline our perspective on the development of this topic with respect to interconnection networks. [ABSTRACT FROM AUTHOR]

Diagnosability is an important topic in analyzing vulnerability and resilience issues of interconnection networks. In this short commentary, we outline the development of this topic. [ABSTRACT FROM AUTHOR]

We derive a general upper bound of the $$R_h$$ -restricted connectivity for the arrangement graph, namely the minimum cardinality of a vertex set, whose removal disconnects the graph, but every remaining vertex has at least $$h ({\ge }0)$$ neighbors in the survival graph. We show that this upper bound is exact when $$h \in [0, 2]$$ and provide an asymptotic lower bound for the cases where $$h\ge 3$$ . [ABSTRACT FROM AUTHOR]

The conditional diagnosability is an important measure of reliability of interconnection networks. Much progress has been made in the past decade. By consolidating various results, a general scheme can be developed to solve the conditional diagnosability problem for many important classes of interconnection networks; thus eliminating various ad-hoc methods used in earlier studies. The buttery network is an important interconnection network and it has been rediscovered multiple times by different authors. The hyper-buttery network is a graph that amalgamates the buttery network and the hypercube. In this paper, we solve the conditional diagnosability problem for these hyper-buttery networks and their generalizations. [ABSTRACT FROM AUTHOR]

We propose the complete cubic network structure to extend the existing class of hierarchical cubic networks, and establish a general connectivity result which states that the surviving graph of a complete cubic network, when a linear number of vertices are removed, consists of a large (connected) component and a number of smaller components which altogether contain a limited number of vertices. As applications, we characterize several fault-tolerance properties for the complete cubic network, including its restricted connectivity, i.e., the size of a minimum vertex cut such that the degree of every vertex in the surviving graph has a guaranteed lower bound; its cyclic vertex-connectivity, i.e., the size of a minimum vertex cut such that at least two components in the surviving graph contain a cycle; its component connectivity, i.e., the size of a minimum vertex cut whose removal leads to a certain number of components in its surviving graph; and its conditional diagnosability, i.e., the maximum number of faulty vertices that can be detected via a self-diagnostic process, in terms of the common Comparison Diagnosis model. [ABSTRACT FROM AUTHOR]

We count the shortest paths, not necessarily disjoint, between any two vertices in an (n, k)-star graph by counting the minimum factorizations of a permutation in terms of the transpositions corresponding to edges in that graph. This result generalizes a previous one for the star graph, and can be applied to obtain the number of the shortest paths between a pair of vertices in some of the other structures closely related to the (n, k)-star graph, such as the alternating group networks. Furthermore, the techniques made use of in this paper can be applied to solve the same problem for some of the other structures such as the arrangement graph. [ABSTRACT FROM AUTHOR]

Nano-precipitates with tripled periodicity along the c-axis are observed in a Ca-rich dolomite sample from Proterozoic carbonate rocks with 'molar tooth' structure. This observation is consistent with previous description of d reflections. High-angle annular dark-field STEM imaging (or Z-contrast imaging) that avoids dynamic diffraction as seen in electron diffraction and high-resolution TEM imaging modes, confirms that d reflections correspond to nanoscale precipitates aligned parallel to (001) of the host dolomite. The lamellae precipitates have a cation ordering sequence of Ca-Ca-Mg-Ca-Ca- Mg along the c direction resulting in a chemical composition of Ca0.67Mg0.33CO3. This superstructure is attributed to the extra or d reflections, thus is referred to as the d superstructure in this study. The structure can be simply described as interstratified calcite/dolomite. The crystal structure of the d superstructure calculated from density functional theory (DFT) has a space group of P31c and has a and c unit-cell parameters of 4.879 and 16.260 Å, respectively, values between those of dolomite and calcite. The detailed structural characteristics and parameters obtained from ab initio calculations are also reported in this paper. The method of combining Z-contrast imaging and ab initio calculations can be used for solving structures of other nano-precipitates and nano-phases. [ABSTRACT FROM AUTHOR]

We suggest the notion ofH-centred surface area of a graph G, whereHis a subgraph ofG, i.e.the number of vertices in G at a certain distance from H, and focus on the special case whenHis a length two path to derive an explicit formula for the length two path-centred surface areas of the general and scalable arrangement graph. [ABSTRACT FROM AUTHOR]

We discuss the notion of $$H$$ - centered surface area of a graph $$G$$ , where $$H$$ is a subgraph of $$G$$ , i.e., the number of vertices in $$G$$ at a certain distance from $$H$$ , and focus on the special case when $$H$$ is a length two path to derive an explicit formula for the length two path centered surface area of the general and scalable arrangement graph, following a generating function approach. [ABSTRACT FROM AUTHOR]

We suggest the notion of the edge-centered surface area for an interconnection network, which generalizes the usual notion of surface area of a network centered at a vertex. Following an elementary approach, we derive an explicit formula expression of the edge-centered surface area for the general arrangement graph. [ABSTRACT FROM AUTHOR]

Let G be a graph. Then $${T\subseteq V(G)}$$ is called a cyclic vertex-cut if G − T is disconnected and at least two components in G − T contain a cycle. The cyclic vertex-connectivity is the size of a smallest cyclic vertex-cut. In this paper, we determine this number for Cayley graphs generated by transposition trees as well as classify all the minimum cyclic vertex-cuts. [ABSTRACT FROM AUTHOR]

An important and interesting parameter of an interconnection network is the number of vertices of a specific distance from a specific vertex. This is known as the surface area or the Whitney number of the second kind. It turns out that, in some applications, the number of vertices of a specific distance from a subgraph H is also important. A fundamental starting point is to consider the number of vertices of a specific distance from an edge, which is called the edge surface area. In this paper, we give an explicit formula for the edge surface area of arrangement graphs via the generating function technique. As a direct consequence, it will also provide such explicit formulas for star graphs, alternating group graphs and split stars. [ABSTRACT FROM AUTHOR]

The surface area of a communication network centered at a certain vertex, i.e., the number of vertices at the same distance from this given vertex within such a network, provides an important measurement of the broadcasting and other intercommunication capabilities of this network and can find several other applications in network studies. Following a generating function approach, we derive a closed-form expression of the surface area of the recently much discussed augmented cube network and its average distance. [ABSTRACT FROM AUTHOR]

We derive an explicit formula for the surface area of the arrangement graph, i.e. the number of vertices at a certain distance from the identity vertex in such a graph. We also present such formulas for the star graph, the alternating group graph, and the split-star graph, via their respective structural relationship to the arrangement graph. [ABSTRACT FROM AUTHOR]

An important and interesting parameter of an interconnection network is the number of vertices of a specific distance from a specific vertex. This is known as the surface area or the Whitney number of the second kind. In this paper, we give explicit formulas for the surface areas of the (n, k)-star graphs and the arrangement graphs via the generating function technique. As a direct consequence, these formulas will also provide such explicit formulas for the star graphs, the alternating group graphs and the split-stars since these graphs are related to the (n, k)-star graphs and the arrangement graphs. In addition, we derive the average distances for these graphs. [ABSTRACT FROM AUTHOR]

In this short note, we use a generating function to give an explicit formula for the surface area of the star graphs. [ABSTRACT FROM AUTHOR]

The class of alternating group networks was introduced in the late 1990's as an alternative to the alternating group graphs as interconnection networks. Recently, additional properties for the alternating group networks have been published. In particular, Zhou et al., J. Supercomput (), doi:, was published very recently in this journal. We show that this so-called new interconnection topology is in fact isomorphic to the ( n, n−2)-star, a member of the well-known ( n, k)-stars, 1≤ k≤ n−1, a class of popular networks proposed earlier for which a large amount of work have already been done. Specifically, the problem in Zhou et al., J. Supercomput (), doi:, was addressed in Lin and Duh, Inf. Sci. 178(3), 788-801, , when k = n−2. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the author discusses the topics include interconnection networks; class of hypergraphs; and diagnosability of networks.