A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent ...A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.展开更多
If is a permutation of , the graph has vertices where xy is an edge of if and only if (x, y) or (y, x) is an inversion of . Any graph isomorphic to is called a permutation graph. In 1967 Gallai characterized permutati...If is a permutation of , the graph has vertices where xy is an edge of if and only if (x, y) or (y, x) is an inversion of . Any graph isomorphic to is called a permutation graph. In 1967 Gallai characterized permutation graphs in terms of forbidden induced subgraphs. In 1971 Pnueli, Lempel, and Even showed that a graph is a permutation graph if and only if both the graph and its complement have transitive orientations. In 2010 Limouzy characterized permutation graphs in terms of forbidden Seidel minors. In this paper, we characterize permutation graphs in terms of a cohesive order of its vertices. We show that only the caterpillars are permutation graphs among the trees. A simple method of constructing permutation graphs is also presented here.展开更多
An L（2, 1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all nonnegative integers such that ｜f（x） - f（y）｜ 〉 2 if d（x, y） = 1 and ｜f（x）-f（y）｜ ≥ 1 ifd（x, y） = 2. The ...An L（2, 1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all nonnegative integers such that ｜f（x） - f（y）｜ 〉 2 if d（x, y） = 1 and ｜f（x）-f（y）｜ ≥ 1 ifd（x, y） = 2. The L（2, 1）-labeling number λ（G） of G is the smallest number k such that G has an L（2, 1）-labeling with max{f（v） ： v ∈ V（G）} = k. We study the L（3, 2, 1）-labeling which is a generalization of the L（2, 1）-labeling on the graph formed by the （Cartesian） product and composition of 3 graphs and derive the upper bounds of λ3（G） of the graph.展开更多
Social engineering has posed a serious threat to cyberspace security.To protect against social engineering attacks,a fundamental work is to know what constitutes social engineering.This paper first develops a domain o...Social engineering has posed a serious threat to cyberspace security.To protect against social engineering attacks,a fundamental work is to know what constitutes social engineering.This paper first develops a domain ontology of social engineering in cybersecurity and conducts ontology evaluation by its knowledge graph application.The domain ontology defines 11 concepts of core entities that significantly constitute or affect social engineering domain,together with 22 kinds of relations describing how these entities related to each other.It provides a formal and explicit knowledge schema to understand,analyze,reuse and share domain knowledge of social engineering.Furthermore,this paper builds a knowledge graph based on 15 social engineering attack incidents and scenarios.7 knowledge graph application examples(in 6 analysis patterns)demonstrate that the ontology together with knowledge graph is useful to 1)understand and analyze social engineering attack scenario and incident,2)find the top ranked social engineering threat elements(e.g.the most exploited human vulnerabilities and most used attack mediums),3)find potential social engineering threats to victims,4)find potential targets for social engineering attackers,5)find potential attack paths from specific attacker to specific target,and 6)analyze the same origin attacks.展开更多
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we...The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.展开更多
云计算与大数据时代的到来促进了Web服务的发展。由于用户需求的复杂性,单个服务无法满足要求时,可将多个服务组合在一起提供解决方案。然而云中存在大量服务,查找合适的服务组合成为一个非确定性多项式(NP,non-deterministic polynomi...云计算与大数据时代的到来促进了Web服务的发展。由于用户需求的复杂性,单个服务无法满足要求时,可将多个服务组合在一起提供解决方案。然而云中存在大量服务,查找合适的服务组合成为一个非确定性多项式(NP,non-deterministic polynomial)难问题。文章提出了一种利用图数据库解决组合问题的方法,通过构建基于有向二分图的服务组合图,对服务进行预组合并存储在Neo4j图数据库中,使用最少服务数组合查询和Dijkstra搜索算法来寻找服务数量最少或服务质量(QoS,quality of service)优化解。此外,能够根据服务的可用性对图数据库进行删除、添加、更新。实验结果表明,该方法能够在较短时间内在图数据库中寻找到满足用户需求的服务组合。展开更多
基金supported by National Natural Science Foundation of China(No.11571091)Natural Science Foundation of Hebei Province,China(No.F2019205147)Innovation Program of Hebei Normal University,China(No.CXZZSS2020050).
文摘A generalized strongly regular graphof grade p,as anew generalization of strongly regular graphs,is a regular graph such that the number of common neighbours of both any two adjacent vertices and any two non-adjacent vertices takes on p distinct values.For any vertex u of a generalized strongly regular graph of grade 2 with parameters(n,k;a_(1),a_(2);c_(1),c_(2)),if the number of the vertices that are adjacent to u and share ai(i=1,2)common neighbours with u,or are non-adjacent to u and share c,(i=1,2)common neighbours with is independent of the choice of the vertex u,then the generalized strongly regular graph of grade 2 is free.In this paper,we investigate the generalized strongly regular graph of grade 2 with parameters(n,k;k-1,a_(2);k-1,c_(2))and provide the sufficient and necessary conditions for the existence of a family of free generalized strongly regular graphs of grade 2.
文摘If is a permutation of , the graph has vertices where xy is an edge of if and only if (x, y) or (y, x) is an inversion of . Any graph isomorphic to is called a permutation graph. In 1967 Gallai characterized permutation graphs in terms of forbidden induced subgraphs. In 1971 Pnueli, Lempel, and Even showed that a graph is a permutation graph if and only if both the graph and its complement have transitive orientations. In 2010 Limouzy characterized permutation graphs in terms of forbidden Seidel minors. In this paper, we characterize permutation graphs in terms of a cohesive order of its vertices. We show that only the caterpillars are permutation graphs among the trees. A simple method of constructing permutation graphs is also presented here.
文摘An L（2, 1）-labeling of a graph G is a function f from the vertex set V（G） to the set of all nonnegative integers such that ｜f（x） - f（y）｜ 〉 2 if d（x, y） = 1 and ｜f（x）-f（y）｜ ≥ 1 ifd（x, y） = 2. The L（2, 1）-labeling number λ（G） of G is the smallest number k such that G has an L（2, 1）-labeling with max{f（v） ： v ∈ V（G）} = k. We study the L（3, 2, 1）-labeling which is a generalization of the L（2, 1）-labeling on the graph formed by the （Cartesian） product and composition of 3 graphs and derive the upper bounds of λ3（G） of the graph.
基金the National Key Research and Development Program of China(2017YFB0802804)the Joint Fund of the National Natural Science Foundation of China(U1766215).
文摘Social engineering has posed a serious threat to cyberspace security.To protect against social engineering attacks,a fundamental work is to know what constitutes social engineering.This paper first develops a domain ontology of social engineering in cybersecurity and conducts ontology evaluation by its knowledge graph application.The domain ontology defines 11 concepts of core entities that significantly constitute or affect social engineering domain,together with 22 kinds of relations describing how these entities related to each other.It provides a formal and explicit knowledge schema to understand,analyze,reuse and share domain knowledge of social engineering.Furthermore,this paper builds a knowledge graph based on 15 social engineering attack incidents and scenarios.7 knowledge graph application examples(in 6 analysis patterns)demonstrate that the ontology together with knowledge graph is useful to 1)understand and analyze social engineering attack scenario and incident,2)find the top ranked social engineering threat elements(e.g.the most exploited human vulnerabilities and most used attack mediums),3)find potential social engineering threats to victims,4)find potential targets for social engineering attackers,5)find potential attack paths from specific attacker to specific target,and 6)analyze the same origin attacks.
基金This work is partially supported by National Natural Science foundation of China Doctoral foundation of the Education Committee of China.
文摘The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. Akiyama, Exoo and Harary conjectured that la(G) = [△(G)+1/2] for any regular graph G. In this paper, we prove the conjecture for some composition graphs, in particular, for complete multipartite graphs.
文摘云计算与大数据时代的到来促进了Web服务的发展。由于用户需求的复杂性,单个服务无法满足要求时,可将多个服务组合在一起提供解决方案。然而云中存在大量服务,查找合适的服务组合成为一个非确定性多项式(NP,non-deterministic polynomial)难问题。文章提出了一种利用图数据库解决组合问题的方法,通过构建基于有向二分图的服务组合图,对服务进行预组合并存储在Neo4j图数据库中,使用最少服务数组合查询和Dijkstra搜索算法来寻找服务数量最少或服务质量(QoS,quality of service)优化解。此外,能够根据服务的可用性对图数据库进行删除、添加、更新。实验结果表明,该方法能够在较短时间内在图数据库中寻找到满足用户需求的服务组合。
