A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulan...A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulant.The rank of a graph is defined to be the rank of its adjacency matrix.This importance of the rank,due to applications in physics,chemistry and combinatorics.In this paper,using Ramanujan sums,we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.展开更多
The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(...The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(2).In this paper,integral generalized Cayley graphs on finite abelian groups are characterized,using the characterization of the spectra of integral Cayley graphs.As an application,the integral generalized Cayley graphs on Z_(p)×Z_(q) and Z2n are investigated,where p and q are odd prime numbers.展开更多
The research aims to develop an automatic Question Answering system,in particular Why and How questions,on community web-boards to support ordinary people in preliminary diagnosis and problem solving,such as plant dis...The research aims to develop an automatic Question Answering system,in particular Why and How questions,on community web-boards to support ordinary people in preliminary diagnosis and problem solving,such as plant disease problems.The research includes two main problems:Why and How question identification and Why and How answer determination,where Why and How questions are based on explanations.Therefore,the research applies machine learning techniques for question type identification.We also propose an integrated causality graph with extracted procedural knowledge from text to determine the visualized answers based on the information retrieval technique.The experiment shows the Question Answering system can achieve answers at Rank 1 with 91.1%and 88.9%correctness for Why questions and How questions,respectively.展开更多
基金Foundation item： Supported by Hunan Provincial Natural Science Foundation（13JJ3118）
文摘A graph is called an integral graph if it has an integral spectrum i.e.,all eigenvalues are integers.A graph is called circulant graph if it is Cayley graph on the circulant group,i.e.,its adjacency matrix is circulant.The rank of a graph is defined to be the rank of its adjacency matrix.This importance of the rank,due to applications in physics,chemistry and combinatorics.In this paper,using Ramanujan sums,we study the rank of integral circulant graphs and gave some simple computational formulas for the rank and provide an example which shows the formula is sharp.
基金supported by the National Natural Science Foundation of China(No.12271311,12101410,12201414)Taishan Scholars Program of Shandong Province.
文摘The spectra of generalized Cayley graphs of finite abelian groups are investigated in this paper.For a generalized Cayley graph X of a finite group G,the canonical double covering of X is the direct product X×K_(2).In this paper,integral generalized Cayley graphs on finite abelian groups are characterized,using the characterization of the spectra of integral Cayley graphs.As an application,the integral generalized Cayley graphs on Z_(p)×Z_(q) and Z2n are investigated,where p and q are odd prime numbers.
基金The research is supported by Thai Research Fund 2012(MRG5580030).
文摘The research aims to develop an automatic Question Answering system,in particular Why and How questions,on community web-boards to support ordinary people in preliminary diagnosis and problem solving,such as plant disease problems.The research includes two main problems:Why and How question identification and Why and How answer determination,where Why and How questions are based on explanations.Therefore,the research applies machine learning techniques for question type identification.We also propose an integrated causality graph with extracted procedural knowledge from text to determine the visualized answers based on the information retrieval technique.The experiment shows the Question Answering system can achieve answers at Rank 1 with 91.1%and 88.9%correctness for Why questions and How questions,respectively.
