This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study ...This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.展开更多
Let G = Γ(S) be a semigroup graph, i.e., a zero-divisor graph of a semigroup S with zero element 0. For any adjacent vertices x, y in G, denote C(x,y) = {z∈V(G) | N (z) = {x,y}}. Assume that in G there exi...Let G = Γ(S) be a semigroup graph, i.e., a zero-divisor graph of a semigroup S with zero element 0. For any adjacent vertices x, y in G, denote C(x,y) = {z∈V(G) | N (z) = {x,y}}. Assume that in G there exist two adjacent vertices x, y, a vertex s∈C(x,y) and a vertex z such that d (s,z) = 3. This paper studies algebraic properties of S with such graphs G = Γ(S), giving some sub-semigroups and ideals of S. It constructs some classes of such semigroup graphs and classifies all semigroup graphs with the property in two cases.展开更多
基于图论方法提出了一种新的证据信任模型(graph theory based evidential trust model,GTETM),解决了现有证据信任模型中普遍存在的在信任聚合过程中缺少对信任链之间依赖关系的有效处理等引起的模型性能下降问题.同时,GTETM在建模实...基于图论方法提出了一种新的证据信任模型(graph theory based evidential trust model,GTETM),解决了现有证据信任模型中普遍存在的在信任聚合过程中缺少对信任链之间依赖关系的有效处理等引起的模型性能下降问题.同时,GTETM在建模实体的信任度时区分实体的服务信任度与反馈信任度,并在证据理论框架下提出两种不同的信任传递方法,增强了模型抵抗恶意推荐攻击的能力.仿真实验表明,与已有信任度量模型相比,GTETM具有更强的抑制策略欺骗及共谋行为的能力,在信任度量准确性方面也有较大提高.展开更多
文摘This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ℤ<sub>n</sub> modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.
文摘Let G = Γ(S) be a semigroup graph, i.e., a zero-divisor graph of a semigroup S with zero element 0. For any adjacent vertices x, y in G, denote C(x,y) = {z∈V(G) | N (z) = {x,y}}. Assume that in G there exist two adjacent vertices x, y, a vertex s∈C(x,y) and a vertex z such that d (s,z) = 3. This paper studies algebraic properties of S with such graphs G = Γ(S), giving some sub-semigroups and ideals of S. It constructs some classes of such semigroup graphs and classifies all semigroup graphs with the property in two cases.
文摘基于图论方法提出了一种新的证据信任模型(graph theory based evidential trust model,GTETM),解决了现有证据信任模型中普遍存在的在信任聚合过程中缺少对信任链之间依赖关系的有效处理等引起的模型性能下降问题.同时,GTETM在建模实体的信任度时区分实体的服务信任度与反馈信任度,并在证据理论框架下提出两种不同的信任传递方法,增强了模型抵抗恶意推荐攻击的能力.仿真实验表明,与已有信任度量模型相比,GTETM具有更强的抑制策略欺骗及共谋行为的能力,在信任度量准确性方面也有较大提高.
