A First Course in Graph Theory and Combinatorics: Second Edition

This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick's theorem on areas of lattice polygons and Graham-Pollak's work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.

本書討論了圖論的起源，從它在娛樂數學中的謙卑開始，到現代的通信網絡建模，正如許多互聯網搜索引擎使用的世界網絡圖所證明的那樣。本書的第二版包括了關於符號鄰接矩陣理論的最新發展，包括對敏感性猜想的證明和拉馬努金圖論的理論。此外，本書還討論了像皮克定理（Pick's theorem）關於格點多邊形面積和格雷厄姆-波拉克（Graham-Pollak）關於圖的地址的工作等主題。圖的概念在數學和工程中是基礎，因為它方便地編碼了各種關係，並促進了許多理論和實際問題的組合分析。本書適合高年級本科生或初級研究生的一學期課程使用。

Sebastian M. Cioaba is Professor at the Department of Mathematical Sciences, University of Delaware, Newark, USA. After his undergraduate studies in mathematics and computer science at the University of Bucharest, Romania, he obtained his Ph.D. in Mathematics at Queen's University at Kingston, Canada. Following postdocs at UC San Diego and the University of Toronto, Sebastian started his teaching position at the University of Delaware in 2009. His research interests are in spectral graph theory, algebraic combinatorics, and their connections and applications to other areas of mathematics and science. He is on the editorial board of several journals including Discrete Mathematics, Linear Algebra and its Applications, and Electronic Journal of Linear Algebra. He has organized several conferences in algebraic combinatorics and spectral graph theory. Sebastian has supervised 5 Ph.D. students, 2 M.Sc. students, 3 undergraduate senior theses, and over 20 summer research students. He has published more than 60 papers, and his research has been supported by NSF, NSA, NSERC, Simons Foundation, IDex Bordeaux, and Japan Society for Promotion of Science.

M. Ram Murty is Queen's Research Chair and A.V. Douglas Distinguished University Professor at Queen's University, in Kingston, Ontario, Canada. He obtained his Ph.D. from Massachusetts Institute of Technology, USA, in 1980 and subsequently held positions at the Institute for Advanced Study in Princeton, Tata Institute for Fundamental Research in Mumbai, and McGill University in Montreal. He has authored more than 250 research papers and written more than a dozen mathematical textbooks. His monograph, Non-vanishing of L-functions and Applications, written jointly with Prof. V. Kumar Murty, won the 1996 Balaguer Prize. Ram is Fellow of the Royal Society of Canada, Fellow of the American Mathematical Society, and Fellow of the Indian National Science Academy, India. He also teaches Indian philosophy at Queen's University and has authored Indian Philosophy: An Introduction, published by Broadview Press.

Sebastian M. Cioaba是美國紐華克特拉華大學數學科學系的教授。他在羅馬尼亞布加勒斯特大學修讀數學和計算機科學的本科學位後，於加拿大金士頓女王大學獲得數學博士學位。在加州大學聖地亞哥分校和多倫多大學進行博士後研究後，Sebastian於2009年開始在特拉華大學擔任教職。他的研究興趣包括光譜圖論、代數組合學以及它們與數學和科學其他領域的聯繫和應用。他是《離散數學》、《線性代數及其應用》和《電子線性代數期刊》等多個期刊的編輯委員會成員。他曾組織過多個代數組合學和光譜圖論的會議。Sebastian指導過5名博士生、2名碩士生、3篇本科畢業論文以及20多名暑期研究生。他發表了60多篇論文，並獲得了美國國家科學基金會、國家安全局、加拿大自然科學與工程研究委員會、Simons基金會、IDex Bordeaux和日本學術振興會的研究資助。

M. Ram Murty是加拿大安大略省金士頓女王大學的皇后研究講座教授和A.V. Douglas傑出大學教授。他於1980年在美國麻省理工學院獲得博士學位，隨後在普林斯頓高等研究院、孟買塔塔基礎研究所和蒙特利爾麥吉爾大學擔任職位。他撰寫了250多篇研究論文，並編寫了十多本數學教科書。他與V. Kumar Murty教授合著的專著《L-函數的非零性及其應用》獲得了1996年的Balaguer獎。Ram是加拿大皇家學會、美國數學學會和印度國家科學院的院士。他還在女王大學教授印度哲學，並出版了Broadview Press出版的《印度哲學導論》。