Gary Chartrand is professor emeritus at Western Michigan University. He was awarded all three of his university degrees in mathematics from Michigan State University. His main interest in mathematics has always been graph theory.He has authored or co-authored over 300 research articles in graph theory. He served as the first managing editor of the Journal of Graph Theory (for seven years) and was a member of the editorial boards of the Journal of Graph Theory and Discrete Mathematics. He served as a vice president of the Institute of Combinatorics and Its Applications. He directed the dissertations of 22 doctoral students at Western Michigan University.He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He also received an award as managing editor of the best new journal (Journal of Graph Theory) by the Association of American Publishers in the scientific, medical, and technical category.Heather Jordon earned her PhD in mathematics from Western Michigan University in 1996 under the direction of Gary Chartrand. She is currently an Associate Editor for Mathematical Reviews, produced by the American Mathematical Society.Vincent Vatter earned his PhD in mathematics from Rutgers University in 2006, studying under Doron Zeilberger. Prior to that, he received his bachelor's degree in mathematics from Michigan State University in 2001. Currently, he is a professor of mathematics at the University of Florida, where he resides with his two daughters, Madison and Vienna. He has authored or co-authored over 60 research articles in enumerative combinatorics, graph theory, order theory, and theoretical computer science, and has directed the dissertations of five doctoral students.Ping Zhang earned her PhD in mathematics from Michigan State University. After spending a year at the University of Texas at El Paso, she joined Western Michigan University, where she currently serves as a professor. In 2017, she was named a Distinguished University Faculty Scholar. Her primary research interests are in algebraic combinatorics and graph theory.Dr. Zhang has co-authored six textbooks, notably Graphs & Digraphs and Chromatic Graph Theory, and is a co-editor of The Handbook of Graph Theory, Second Edition, all published by CRC Press. She has also authored or co-authored over 340 research articles and given more than 80 talks at various universities and conferences. At Western Michigan University, she has directed the dissertations of 26 doctoral students.

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• 1 Graphs1.1 Fundamentals1.2 Isomorphism1.3 Families of graphs1.4 Operations on graphs1.5 Degree sequences1.6 Path and cycles1.7 Connected graphs and distance1.8 Trees and forests1.9 Multigraphs and pseudographs2 Digraphs2.1 Fundamentals2.2 Strongly connected digraphs2.3 Tournaments2.4 Score sequences3 Traversability3.1 Eulerian graphs and digraphs3.2 Hamiltonian graphs3.3 Hamiltonian digraphs3.4 Highly hamiltonian graphs3.5 Graph powers4 Connectivity4.1 Cut-vertices, bridges, and blocks4.2 Vertex connectivity4.3 Edge-connectivity4.4 Menger's theorem5 Planarity5.1 Euler's formula5.2 Characterizations of planarity5.3 Hamiltonian planar graphs5.4 The crossing number of a graph6 Coloring6.1 Vertex coloring6.2 Edge coloring6.3 Critical and perfect graphs6.4 Maps and planar graphs7 Flows7.1 Networks7.2 Max-flow min-cut theorem7.3 Menger's theorems for digraphs7.4 A connection to coloring8 Factors and covers8.1 Matchings and 1-factors8.2 Independence and covers8.3 Domination8.4 Factorizations and decompositions8.5 Labelings of graphs9 Extremal graph theory9.1 Avoiding a complete graph9.2 Containing cycles and trees9.3 Ramsey theory9.4 Cages and Moore graphs10 Embeddings10.1 The genus of a graph10.2 2-Cell embeddings of graphs10.3 The maximum genus of a graph10.4 The graph minor theorem11 Graphs and algebra11.1 Graphs and matrices11.2 The automorphism group11.3 Cayley color graphs11.4 The reconstruction problem

Gary Chartrand is professor emeritus at Western Michigan University. He was awarded all three of his university degrees in mathematics from Michigan State University. His main interest in mathematics has always been graph theory.He has authored or co-authored over 300 research articles in graph theory. He served as the first managing editor of the Journal of Graph Theory (for seven years) and was a member of the editorial boards of the Journal of Graph Theory and Discrete Mathematics. He served as a vice president of the Institute of Combinatorics and Its Applications. He directed the dissertations of 22 doctoral students at Western Michigan University.He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He also received an award as managing editor of the best new journal (Journal of Graph Theory) by the Association of American Publishers in the scientific, medical, and technical category.Heather Jordon earned her PhD in mathematics from Western Michigan University in 1996 under the direction of Gary Chartrand. She is currently an Associate Editor for Mathematical Reviews, produced by the American Mathematical Society.Vincent Vatter earned his PhD in mathematics from Rutgers University in 2006, studying under Doron Zeilberger. Prior to that, he received his bachelor's degree in mathematics from Michigan State University in 2001. Currently, he is a professor of mathematics at the University of Florida, where he resides with his two daughters, Madison and Vienna. He has authored or co-authored over 60 research articles in enumerative combinatorics, graph theory, order theory, and theoretical computer science, and has directed the dissertations of five doctoral students.Ping Zhang earned her PhD in mathematics from Michigan State University. After spending a year at the University of Texas at El Paso, she joined Western Michigan University, where she currently serves as a professor. In 2017, she was named a Distinguished University Faculty Scholar. Her primary research interests are in algebraic combinatorics and graph theory.Dr. Zhang has co-authored six textbooks, notably Graphs & Digraphs and Chromatic Graph Theory, and is a co-editor of The Handbook of Graph Theory, Second Edition, all published by CRC Press. She has also authored or co-authored over 340 research articles and given more than 80 talks at various universities and conferences. At Western Michigan University, she has directed the dissertations of 26 doctoral students.

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• 1 Graphs1.1 Fundamentals1.2 Isomorphism1.3 Families of graphs1.4 Operations on graphs1.5 Degree sequences1.6 Path and cycles1.7 Connected graphs and distance1.8 Trees and forests1.9 Multigraphs and pseudographs2 Digraphs2.1 Fundamentals2.2 Strongly connected digraphs2.3 Tournaments2.4 Score sequences3 Traversability3.1 Eulerian graphs and digraphs3.2 Hamiltonian graphs3.3 Hamiltonian digraphs3.4 Highly hamiltonian graphs3.5 Graph powers4 Connectivity4.1 Cut-vertices, bridges, and blocks4.2 Vertex connectivity4.3 Edge-connectivity4.4 Menger's theorem5 Planarity5.1 Euler's formula5.2 Characterizations of planarity5.3 Hamiltonian planar graphs5.4 The crossing number of a graph6 Coloring6.1 Vertex coloring6.2 Edge coloring6.3 Critical and perfect graphs6.4 Maps and planar graphs7 Flows7.1 Networks7.2 Max-flow min-cut theorem7.3 Menger's theorems for digraphs7.4 A connection to coloring8 Factors and covers8.1 Matchings and 1-factors8.2 Independence and covers8.3 Domination8.4 Factorizations and decompositions8.5 Labelings of graphs9 Extremal graph theory9.1 Avoiding a complete graph9.2 Containing cycles and trees9.3 Ramsey theory9.4 Cages and Moore graphs10 Embeddings10.1 The genus of a graph10.2 2-Cell embeddings of graphs10.3 The maximum genus of a graph10.4 The graph minor theorem11 Graphs and algebra11.1 Graphs and matrices11.2 The automorphism group11.3 Cayley color graphs11.4 The reconstruction problem

Gary Chartrand is professor emeritus at Western Michigan University. He was awarded all three of his university degrees in mathematics from Michigan State University. His main interest in mathematics has always been graph theory.He has authored or co-authored over 300 research articles in graph theory. He served as the first managing editor of the Journal of Graph Theory (for seven years) and was a member of the editorial boards of the Journal of Graph Theory and Discrete Mathematics. He served as a vice president of the Institute of Combinatorics and Its Applications. He directed the dissertations of 22 doctoral students at Western Michigan University.He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He also received an award as managing editor of the best new journal (Journal of Graph Theory) by the Association of American Publishers in the scientific, medical, and technical category.Heather Jordon earned her PhD in mathematics from Western Michigan University in 1996 under the direction of Gary Chartrand. She is currently an Associate Editor for Mathematical Reviews, produced by the American Mathematical Society.Vincent Vatter earned his PhD in mathematics from Rutgers University in 2006, studying under Doron Zeilberger. Prior to that, he received his bachelor's degree in mathematics from Michigan State University in 2001. Currently, he is a professor of mathematics at the University of Florida, where he resides with his two daughters, Madison and Vienna. He has authored or co-authored over 60 research articles in enumerative combinatorics, graph theory, order theory, and theoretical computer science, and has directed the dissertations of five doctoral students.Ping Zhang earned her PhD in mathematics from Michigan State University. After spending a year at the University of Texas at El Paso, she joined Western Michigan University, where she currently serves as a professor. In 2017, she was named a Distinguished University Faculty Scholar. Her primary research interests are in algebraic combinatorics and graph theory.Dr. Zhang has co-authored six textbooks, notably Graphs & Digraphs and Chromatic Graph Theory, and is a co-editor of The Handbook of Graph Theory, Second Edition, all published by CRC Press. She has also authored or co-authored over 340 research articles and given more than 80 talks at various universities and conferences. At Western Michigan University, she has directed the dissertations of 26 doctoral students.

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• 1 Graphs1.1 Fundamentals1.2 Isomorphism1.3 Families of graphs1.4 Operations on graphs1.5 Degree sequences1.6 Path and cycles1.7 Connected graphs and distance1.8 Trees and forests1.9 Multigraphs and pseudographs2 Digraphs2.1 Fundamentals2.2 Strongly connected digraphs2.3 Tournaments2.4 Score sequences3 Traversability3.1 Eulerian graphs and digraphs3.2 Hamiltonian graphs3.3 Hamiltonian digraphs3.4 Highly hamiltonian graphs3.5 Graph powers4 Connectivity4.1 Cut-vertices, bridges, and blocks4.2 Vertex connectivity4.3 Edge-connectivity4.4 Menger's theorem5 Planarity5.1 Euler's formula5.2 Characterizations of planarity5.3 Hamiltonian planar graphs5.4 The crossing number of a graph6 Coloring6.1 Vertex coloring6.2 Edge coloring6.3 Critical and perfect graphs6.4 Maps and planar graphs7 Flows7.1 Networks7.2 Max-flow min-cut theorem7.3 Menger's theorems for digraphs7.4 A connection to coloring8 Factors and covers8.1 Matchings and 1-factors8.2 Independence and covers8.3 Domination8.4 Factorizations and decompositions8.5 Labelings of graphs9 Extremal graph theory9.1 Avoiding a complete graph9.2 Containing cycles and trees9.3 Ramsey theory9.4 Cages and Moore graphs10 Embeddings10.1 The genus of a graph10.2 2-Cell embeddings of graphs10.3 The maximum genus of a graph10.4 The graph minor theorem11 Graphs and algebra11.1 Graphs and matrices11.2 The automorphism group11.3 Cayley color graphs11.4 The reconstruction problem