For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [...For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [ci - cj] ≤1 for any two colors i and j, then c is an equitable edge coloring of G. The coloring c is an equitable adjacent strong edge coloring of G if it is both adjacent strong edge coloring and equitable edge coloring. The least number of colors of such a coloring c is called the equitable adjacent strong chromatic index of G. In this paper, we determine the equitable adjacent strong chromatic index of the joins of paths and cycles. Precisely, we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.展开更多
A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum o...A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y.We say that a graph is antimagic if it has an antimagic labeling.Hartsfield and Ringel conjectured in 1990 that every graph other than 2 K is antimagic.In this paper,we show that the antimagic conjecture is false for the case of disconnected graphs.Furthermore,we find some classes of disconnected graphs that are antimagic and some classes of graphs whose complement are disconnected are antimagic.展开更多
Adding a new vertex to any edge of the complete bipartite graph K2,3 gives a subdivision of K2,3 （6-vertices graph）. In the paper, we get the crossing numbers of the join graph of the specific 6-vertices graph H wit...Adding a new vertex to any edge of the complete bipartite graph K2,3 gives a subdivision of K2,3 （6-vertices graph）. In the paper, we get the crossing numbers of the join graph of the specific 6-vertices graph H with n isolated vertices as well as with the path Pn on n vertices and with the cycle Cn.展开更多
基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且...基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且满足本地化差分隐私的Star-JOIN查询算法LPRR-JOIN(longitudinal path random response for join).该算法充分利用层次树的纵向路径结构与GRR机制,设计一种纵向本地扰动算法LPRR,该算法以所有属性纵向路径上的节点组合作为扰动值域.每个用户把自身元组映射到相应节点组合中,再利用GRR机制对映射后的元组进行本地扰动.为了避免事实表上存在的频率攻击,LPRR-JOIN算法允许每个用户利用阈值τ本地截断自身元组个数,大于τ条元组删减、小于τ条元组补充.为了寻找合适的τ值,LPRR-JOIN算法利用τ-截断带来的偏差与扰动方差构造总体误差函数,通过优化误差目标函数获得τ值;其次结合用户分组策略获得τ值的总体分布,再利用中位数获得合适的τ值.LPRR-JOIN算法与现有算法在3种多关系数据集上进行比较,实验结果表明其响应查询算法优于同类算法.展开更多
基金Supported by the Fundamental Research Funds for the Central Universities(Grant Nos. 2011B019)the National Natural Science Foundation of China (Grant Nos. 10971144+2 种基金1110102011171026)the Natural Science Foundation of Beijing (Grant No. 1102015)
文摘For a proper edge coloring c of a graph G, if the sets of colors of adjacent vertices are distinct, the edge coloring c is called an adjacent strong edge coloring of G. Let ci be the number of edges colored by i. If [ci - cj] ≤1 for any two colors i and j, then c is an equitable edge coloring of G. The coloring c is an equitable adjacent strong edge coloring of G if it is both adjacent strong edge coloring and equitable edge coloring. The least number of colors of such a coloring c is called the equitable adjacent strong chromatic index of G. In this paper, we determine the equitable adjacent strong chromatic index of the joins of paths and cycles. Precisely, we show that the equitable adjacent strong chromatic index of the joins of paths and cycles is equal to the maximum degree plus one or two.
基金Supported by the National Natural Science Foundation of China (10201022,10971144,and 11101020)the Natural Science Foundation of Beijing (1102015)the Fundamental Research Funds for the Central Universities(2011B019)
文摘A labeling of a graph G is a bijection from E（G） to the set {1,2,…,｜E （G）｜ }.A labeling is antimagic if for any distinct vertices x and y,the sum of the labels on edges incident to x is different from the sum of the labels on edges incident to y.We say that a graph is antimagic if it has an antimagic labeling.Hartsfield and Ringel conjectured in 1990 that every graph other than 2 K is antimagic.In this paper,we show that the antimagic conjecture is false for the case of disconnected graphs.Furthermore,we find some classes of disconnected graphs that are antimagic and some classes of graphs whose complement are disconnected are antimagic.
基金Supported by the Natural Science Foundation of Hunan Province(Grant No.2017JJ3251)
文摘Adding a new vertex to any edge of the complete bipartite graph K2,3 gives a subdivision of K2,3 （6-vertices graph）. In the paper, we get the crossing numbers of the join graph of the specific 6-vertices graph H with n isolated vertices as well as with the path Pn on n vertices and with the cycle Cn.
文摘基于本地化差分隐私多关系表示上的Star-JOIN查询已得到研究者广泛关注.现有基于OLH机制与层次树结构的Star-JOIN查询算法存在根节点泄露隐私风险、τ-截断机制没有给出如何选择合适τ值等问题.针对现有算法存在的不足,提出一种有效且满足本地化差分隐私的Star-JOIN查询算法LPRR-JOIN(longitudinal path random response for join).该算法充分利用层次树的纵向路径结构与GRR机制,设计一种纵向本地扰动算法LPRR,该算法以所有属性纵向路径上的节点组合作为扰动值域.每个用户把自身元组映射到相应节点组合中,再利用GRR机制对映射后的元组进行本地扰动.为了避免事实表上存在的频率攻击,LPRR-JOIN算法允许每个用户利用阈值τ本地截断自身元组个数,大于τ条元组删减、小于τ条元组补充.为了寻找合适的τ值,LPRR-JOIN算法利用τ-截断带来的偏差与扰动方差构造总体误差函数,通过优化误差目标函数获得τ值;其次结合用户分组策略获得τ值的总体分布,再利用中位数获得合适的τ值.LPRR-JOIN算法与现有算法在3种多关系数据集上进行比较,实验结果表明其响应查询算法优于同类算法.
