Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty ve...Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 （respectively, 2n - 2fv - 2） can be embedded on Qn,k with fv ＋ f≤ n- 1 when dQn,k （u, v） is odd （respectively, dQ,~,k （u, v） is even）. Secondly, an Q,,k is （n - 2） edgefault-free hyper Hamiltonianaceable when n （ 3） and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv＋f≤2n-4.展开更多
The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive propertie...The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ（s, t）. We prove the result in ECQ（s, t）： if s≥3, t≥3, for any two different vertices, all paths whose lengths are between max{9,「s＋1/2」 ＋「t＋1/2＋4}and 2s＋t＋1？1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ（s, t） is「s＋1/2 」＋「t＋1/2 」＋2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ（s, t） preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.展开更多
Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-stat...Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-state or rainy conditions)without hole scavenging agents.In this work,we developed a class of energy-storage quasi-planar heterojunctions(WO_(3)-Nb_(2)O_(5)-ZnIn_(2)S_(4))with directional paths(low onset potential and well-matched energy band)and embedded morphology.The co-design of embedded and directional paths reduces the carrier transport energy barrier at the composite interface,and increases the interface contact area,thereby achieving highly stable and sensitive dark-state energy storage and photoelectrochemical cathodic protection performance in 3.5 wt.%NaCl solution without hole scavenging agent(Dark-state energy storage efficiency increased by 43%.For carbon steel,the performance retention rate is 99.6%after 500 cycles,the performance retention rate is 89%after 5000 s).展开更多
基金supported by NSFC (11071096, 11171129)NSF of Hubei Province, China (T201103)
文摘Let Qn,k （n 〉 3, 1 〈 k ≤ n - 1） be an n-dimensional enhanced hypercube which is an attractive variant of the hypercube and can be obtained by adding some complementary edges, fv and fe be the numbers of faulty vertices and faulty edges, respectively. In this paper, we give three main results. First, a fault-free path P[u, v] of length at least 2n - 2fv - 1 （respectively, 2n - 2fv - 2） can be embedded on Qn,k with fv ＋ f≤ n- 1 when dQn,k （u, v） is odd （respectively, dQ,~,k （u, v） is even）. Secondly, an Q,,k is （n - 2） edgefault-free hyper Hamiltonianaceable when n （ 3） and k have the same parity. Lastly, a fault-free cycle of length at least 2n - 2fv can be embedded on Qn,k with f~ 〈 n - 1 and fv＋f≤2n-4.
基金This work is supported by the National Natural Science Foundation of China under Grant Nos. 61572337 and 61502328, the Program for Postgraduates Research Innovation in University of Jiangsu Province under Grant No. KYLX16_0126, Collaborative Innovation Center of Novel Software Technology and Industrialization, and tile Natural Science Foundation of tile Jiangsu Higher Education Institutions of China under Grant No. 14KJB520034.
文摘The （s＋t＋1）-dimensional exchanged crossed cube, denoted as ECQ（s, t）, combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ（s, t） has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ（s, t）. We prove the result in ECQ（s, t）： if s≥3, t≥3, for any two different vertices, all paths whose lengths are between max{9,「s＋1/2」 ＋「t＋1/2＋4}and 2s＋t＋1？1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ（s, t） is「s＋1/2 」＋「t＋1/2 」＋2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ（s, t） preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.
基金financially supported by the Henan Province Key R&D and Promotion Project(Technology Research)(NO.232102230011)the Fundamental Research Fund of Henan Academy of Sciences(NO.230618026)+1 种基金Joint Fund of Henan Province Science and Technology R&D Program(NO.225200810120)High-level Talent Research Start-up Project Funding of Henan Academy of Sciences(NOs.231818022 and 232018001).
文摘Constructing a photoanode with both high dark-state protection performance and high stability remains a top priority for photoelectrochemical cathodic protection technology,especially in a marine environment(dark-state or rainy conditions)without hole scavenging agents.In this work,we developed a class of energy-storage quasi-planar heterojunctions(WO_(3)-Nb_(2)O_(5)-ZnIn_(2)S_(4))with directional paths(low onset potential and well-matched energy band)and embedded morphology.The co-design of embedded and directional paths reduces the carrier transport energy barrier at the composite interface,and increases the interface contact area,thereby achieving highly stable and sensitive dark-state energy storage and photoelectrochemical cathodic protection performance in 3.5 wt.%NaCl solution without hole scavenging agent(Dark-state energy storage efficiency increased by 43%.For carbon steel,the performance retention rate is 99.6%after 500 cycles,the performance retention rate is 89%after 5000 s).
