The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path...The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.展开更多
This paper presents a novel methodology for constructing and empirically validating Adaptive Curriculum Graphs(ACGs)designed to generate personalized learning paths(PLPs)within Artificial Intelligence Education Studie...This paper presents a novel methodology for constructing and empirically validating Adaptive Curriculum Graphs(ACGs)designed to generate personalized learning paths(PLPs)within Artificial Intelligence Education Studies.The construction process involves automated concept extraction from diverse educational materials,sophisticated prerequisite relationship modeling,graph assembly,and algorithms for dynamic adaptation based on learner interactions.The empirical validation employs an experimental research design to assess the ACGdriven PLPs against traditional learning approaches.Key findings indicate that the proposed ACG framework significantly improves learning outcomes,enhances student engagement,and increases learner satisfaction.This research contributes a robust,adaptable system for personalized education,offering practical implications for educators and technology developers.The originality of this work lies in its comprehensive approach to building dynamically adaptive curriculum structures and its rigorous empirical validation,addressing existing gaps in the personalized learning landscape.展开更多
基金supported by Natural Sciences Foundation of Guangxi Province(2012GXNSFBA053005)
文摘The P_(k)-path graph P_(k)(G)corresponding to a graph G has for vertices the set of all paths of length k in G.Two vertices are joined by an edge if and only if the intersection of the corresponding paths forms a path of length k-1 in G,and their union forms either a cycle or a path of length k+1.Let Ek={(v,p),p E V(P_(k)(G)),v is an end vertex of p in G},we define total P_(k)-graphs T_(k)(G)as Yk(G)=(V(G)UV(P_(k)(G)),E(G)U E(PI(G))U Ek).In this note,we introduce total P,-graphs Th(G)and study their edge connectivity,as the generaliza-tion of total graphs.
文摘This paper presents a novel methodology for constructing and empirically validating Adaptive Curriculum Graphs(ACGs)designed to generate personalized learning paths(PLPs)within Artificial Intelligence Education Studies.The construction process involves automated concept extraction from diverse educational materials,sophisticated prerequisite relationship modeling,graph assembly,and algorithms for dynamic adaptation based on learner interactions.The empirical validation employs an experimental research design to assess the ACGdriven PLPs against traditional learning approaches.Key findings indicate that the proposed ACG framework significantly improves learning outcomes,enhances student engagement,and increases learner satisfaction.This research contributes a robust,adaptable system for personalized education,offering practical implications for educators and technology developers.The originality of this work lies in its comprehensive approach to building dynamically adaptive curriculum structures and its rigorous empirical validation,addressing existing gaps in the personalized learning landscape.
