The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks.This note shows that the Kautz undirected graph is super edge-connected,and provides a short proo...The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks.This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lü and Zhang's result on super edge-connectivity of the de Bruijn undirected graph.展开更多
Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regu...Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.展开更多
The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, ...The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.展开更多
针对当前图摘要方法压缩率较高,图压缩算法无法直接被用于下游任务分析的问题,提出一种图摘要与图压缩的融合算法,即基于节点相似性分组与图压缩的图摘要算法(GSNSC)。首先,初始化节点为超节点,并根据相似度对超节点分组;其次,将每个组...针对当前图摘要方法压缩率较高,图压缩算法无法直接被用于下游任务分析的问题,提出一种图摘要与图压缩的融合算法,即基于节点相似性分组与图压缩的图摘要算法(GSNSC)。首先,初始化节点为超节点,并根据相似度对超节点分组;其次,将每个组的超节点合并,直到达到指定次数或指定节点数;再次,在超节点之间添加超边和校正边以恢复原始图;最后,对于图压缩部分,判断对每个超节点的邻接边压缩和摘要的代价,并选择二者中代价较小的执行。在Web-NotreDame、Web-Google和Web-Berkstan等6个数据集上进行了图压缩率和图查询实验。实验结果表明,在6个数据集上,与SLUGGER(Scalable Lossless sUmmarization of Graphs with HiERarchy)算法相比,所提算法的压缩率至少降低了23个百分点;与SWeG(Summarization of Web-scale Graphs)算法相比,所提算法的压缩率至少降低了13个百分点;在Web-NotreDame数据集上,所提算法的度误差比SWeG降低了41.6%。以上验证了所提算法具有更好的图压缩率和图查询准确度。展开更多
基金by ANSF( 0 1 0 4 61 0 2 ) and the National Natural Science Foundatim of China ( 1 0 2 71 1 1 4)
文摘The super edge-connectivity of a graph is an important parameter to measure fault-tolerance of interconnection networks.This note shows that the Kautz undirected graph is super edge-connected,and provides a short proof of Lü and Zhang's result on super edge-connectivity of the de Bruijn undirected graph.
文摘Tian and Meng in [Y. Tian and J. Meng, λc -Optimally half vertex transitive graphs with regularity k, Information Processing Letters 109 (2009) 683 - 686] shown that a connected half vertex transitive graph with regularity k and girth g(G) ≥ 6 is cyclically optimal. In this paper, we show that a connected half vertex transitive graph G is super cyclically edge-connected if minimum degree δ(G) ≥ 6 and girth g(G) ≥ 6.
基金the Key Project of the Ministry of Education of China (205073)Research Fund for Doctorial Program of Higher Education (No.20060255006)
文摘The notions of fuzzy (super) pramart are introduced. Then the completeness and separability of metric space are discussed. A necessary and sufficient condition of convergence for fuzzy sequences is provided. Finally, the graph Kuratowski-Mosco convergence and D-convergence of fuzzy (super) pramart and quasi-martingale are studied.
文摘针对当前图摘要方法压缩率较高,图压缩算法无法直接被用于下游任务分析的问题,提出一种图摘要与图压缩的融合算法,即基于节点相似性分组与图压缩的图摘要算法(GSNSC)。首先,初始化节点为超节点,并根据相似度对超节点分组;其次,将每个组的超节点合并,直到达到指定次数或指定节点数;再次,在超节点之间添加超边和校正边以恢复原始图;最后,对于图压缩部分,判断对每个超节点的邻接边压缩和摘要的代价,并选择二者中代价较小的执行。在Web-NotreDame、Web-Google和Web-Berkstan等6个数据集上进行了图压缩率和图查询实验。实验结果表明,在6个数据集上,与SLUGGER(Scalable Lossless sUmmarization of Graphs with HiERarchy)算法相比,所提算法的压缩率至少降低了23个百分点;与SWeG(Summarization of Web-scale Graphs)算法相比,所提算法的压缩率至少降低了13个百分点;在Web-NotreDame数据集上,所提算法的度误差比SWeG降低了41.6%。以上验证了所提算法具有更好的图压缩率和图查询准确度。
