研究生课程教学大纲 课程代码Syllabus of课程名称 Course Class 1100016003 60 Code Hours Course ☑Degree Name Graph Theory and its Application Course ☐Non-Degree Credit 3 Nature ☐Others Semester )Fall/(√)Spring Students (√)Master/(√)Ph.D Discipline Linear Algebra Prerequisites School School of Mathematical Sciences Written by Chun Yang Reviewed by Zhaoyin Xiang Date 2019.5 1.Course Objectives Graph theory is an important and frontier discipline of numerous areas,and it has wide applications.It has been extensively used in physics,chemistry,telecommunication,computer science,electronics and civil engineering,operational research,biogenetics,psychology,sociology, economics,anthropology and etc.Especially,graph theory is a necessary mathematical tool of studying computer science,telecommunication,electronic circuit.By learning this course,one can grasp fundamental concepts and theories of graph theory,understand basic research methods of graph theory and use graph theory to cope with related problems in his/her own major,as well as do adequate preparation for related curriculum. 2.Course Content and Requirements Chapter 1.Basic concepts of graph(8 hr) (1).Teaching contents: a.Graph and simple graph(2 hr); b.Subgraph and operations of graphs,path and connectedness(2 hr); c.Shortest path algorithm,algebraic representation of graph and its characteristic(2 hr); d.Extremal graph,intersection graph and clique graph(2 hr). (2).Teaching requirements: By learning this chapter,students will understand some fundamental results and its relationship between practical problems,grasp the concepts of graph,multigraph,simple graph and subgraphs,as well as degree and its related theories,path and connectedness of graph, algebraic representation of graph. (3).Key points of teaching:Degree sequence of graph,graphic sequence,shortest path and its algorithm (4).Teaching difficulties:Isomorphism of graphs and extremal graph theory.研究生课程教学大纲 9 课程代码 Syllabus of 课程名称 Course Code 1100016003 Course Name Graph Theory and its Application Class Hours 60 Course Nature □√ Degree □Non-Degree □Others Credit 3 Semester ( )Fall/( √ )Spring Students (√) Master/(√) Ph.D Discipline Prerequisites Linear Algebra School School of Mathematical Sciences Written by Chun Yang Reviewed by Zhaoyin Xiang Date 2019. 5 1. Course Objectives Graph theory is an important and frontier discipline of numerous areas, and it has wide applications. It has been extensively used in physics, chemistry, telecommunication, computer science, electronics and civil engineering, operational research, biogenetics, psychology, sociology, economics, anthropology and etc. Especially, graph theory is a necessary mathematical tool of studying computer science, telecommunication, electronic circuit. By learning this course, one can grasp fundamental concepts and theories of graph theory, understand basic research methods of graph theory and use graph theory to cope with related problems in his/her own major, as well as do adequate preparation for related curriculum. 2. Course Content and Requirements Chapter 1. Basic concepts of graph (8 hr) (1). Teaching contents: a. Graph and simple graph (2 hr); b. Subgraph and operations of graphs, path and connectedness (2 hr); c. Shortest path algorithm, algebraic representation of graph and its characteristic (2 hr); d. Extremal graph, intersection graph and clique graph (2 hr). (2). Teaching requirements: By learning this chapter, students will understand some fundamental results and its relationship between practical problems, grasp the concepts of graph, multigraph, simple graph and subgraphs, as well as degree and its related theories, path and connectedness of graph, algebraic representation of graph. (3). Key points of teaching: Degree sequence of graph, graphic sequence, shortest path and its algorithm. (4). Teaching difficulties: Isomorphism of graphs and extremal graph theory