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Harary F. — Graph Theory
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Название: Graph TheoryАвтор: Harary F. Аннотация: There are several reasons for the acceleration of interest in graph theory. It has become fashionable to mention that there are applications of graph theory to some areas of physics, chemistry, communication science, computer technology, electrical and civil engineering, architecture, operational research, genetics, psychology, sociology, economics, anthropology, and linguistics. The theory is also intimately related to many branches of mathematics, including group theory, matrix theory, numerical analysis, probability, topology, and combinatorics. The fact is that graph theory serves as a mathematical model for any system involving a binary relation. Partly because of their diagrammatic representation, graphs have an intuitive and aesthetic appeal. Although there are many results in this field of an elementary nature, there is also an abundance of problems with enough combinatorial subtlety to challenge the most sophisticated mathematician.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1969Количество страниц: 274Добавлена в каталог: 20.11.2009Операции: Положить на полку |
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Предметный указатель
0-chain 37 1-basis 202 1-chain 37 1-skeleton 103 2-lattice 194 3-lattice 194 Achromatic number 144 Acyclic, digraph 200 Acyclic, graph 32 Addition of a line 11 Adjacency matrix, of a digraph 151 202 Adjacency matrix, of a graph 150 Adjacent lines 9 Adjacent points, in a digraph 198 Adjacent points, in a graph 9 Animal 194 Arbitrarily traversable graph 69 Arboricity 90 ARC 10 Automorphism 161 Bigraph 17 Bigraph, complete 17 Bipartite graph 17 Block 26 Block graph 29 Block-cutpoint graph 36 Block-cutpoint graph, tree 37 Boundary 37 Branch 35 Bridge 26 Center 35 Central point 35 Centroid 36 Centroid point 36 Chord 38 Chromatic number, of a graph 127 Chromatic number, of a manifold 135 Chromatic polynomial 146 circuits 40 41 Circumference 13 CLIQUE 20 Clique graph 20 Coarseness 121 Coboundary 38 Cocircuit 41 Cocycle 38 Cocycle basis 38 Cocycle basis, matrix 155 Cocycle basis, rank 39 Cocycle basis, space 38 Color class 126 Color-graph 168 Coloring 126 Coloring of a graph from t colors 145 Coloring of a plane map 131 Coloring, complete 143 Complement 15 Complete bigraph 17 Complete graph 16 Complete n-partite graph 23 Complex, simplicial 7 Component 13 Composite graph 166 Composition, of graphs 22 Composition, of permutation groups 164 Condensation 200 Configuration 181 Configuration, counting series 182 Configuration, group 181 Conjunction, of digraphs 210 Conjunction, of graphs 25 Connected graph 13 Connected, strongly 199 Connected, unilaterally 199 Connected, weakly 199 Connectivity 43 Connectivity, function 45 Connectivity, local 49 Connectivity, pair 45 Contractible 113 Contraction, elementary 112 Contrafunctional digraph 201 CONVERSE 200 Corona 167 Cospectral digraphs 210 Cospectral graphs 158 Cotree 39 Cover, minimum 94 Covering, in a graph 94 Covering, in a matrix 53 Critical graph (color) 141 Critical graph (cover) 98 Critical line (cover) 97 Critical point (cover) 97 Crossing number 122 Cubic graph 15 Cutpoint 26 Cutpoint, graph 30 Cutset 38 Cycle basis 38 Cycle basis, matrix 154 Cycle basis, rank 39 Cycle basis, space 38 Cycle basis, vector 38 Cycle index 181 Cycle, in a digraph 198 Cycle, in a graph 13 Cyclic triple 205 Degree, of a line 171 Degree, of a permutation group 161 Degree, of a point 14 Detour matrix 203 Diameter 14 Digraph 198 Digraph, acyclic 200 Digraph, adjacency matrix of 151 202 Digraph, contrafunctional 201 Digraph, disconnected 199 Digraph, Eulerian 204 Digraph, functional 201 Digraph, line 209 Digraph, primitive 210 Digraph, strong 199 Digraph, trivial 199 Digraph, unilateral 199 Digraph, weak 199 Dimension of a simplex 7 Directed graph 10 Directed line 10 198 Disjoint paths 47 Distance, in a digraph 199 Distance, in a graph 14 Distance, matrix 206 Dual, combinatorial 114 Dual, geometric 113 Eccentricity 35 Elementwise product 203 Embedding 102 Endomorphism 177 Endpoint 15 Eulerian digraph 204 Eulerian graph 64 Eulerian matroid 159 Eulerian trail, in a digraph 204 Eulerian trail, in a graph 64 Exponentiation group 177 Face 103 Face, exterior 103 Factor 84 figure 181 Figure, counting series 182 Fixed point 171 Forest 32 Functional digraph 201 Genus 117 Geodesic 14 girth 13 Graph 7 9 Graph, acyclic 32 Graph, arbitrarily traversable 69 Graph, bipartite 17 Graph, block 29 Graph, block-cutpoint 36 Graph, clique 20 Graph, color- 168 Graph, complement of 15 Graph, complete 16 Graph, complete n-partite 23 Graph, composite 166 Graph, connected 13 Graph, critical 98 141 Graph, cubic 15 Graph, cutpoint 30 Graph, directed 10 Graph, Eulerian 64 Graph, Hamiltonian 65 Graph, identity 161 Graph, infinite 16 Graph, intersection 19 Graph, interval 20 Graph, irreducible 99 Graph, labeled 10 Graph, line 70 Graph, line-critical 98 142 Graph, line-regular 171 Graph, line-symmetric 171 Graph, n-chromatic 127 Graph, n-colorable 127 Graph, n-connected 45 Graph, n-critical (color) 141 Graph, n-factorable 84 Graph, n-line connected 45 Graph, n-line critical (color) 142 Graph, n-regular 174 Graph, n-transitive 173 Graph, n-unitransitive 174 Graph, nonseparable 26 Graph, oriented 10 Graph, outerplanar 106 Graph, planar 102 Graph, plane 102 Graph, point critical (cover) 98 Graph, point-symmetric 171 Graph, prime 166 Graph, reducible 99 Graph, regular 14 Graph, self-complementary 15 Graph, semi-irreducible 99 Graph, subdivision 81 Graph, symmetric 171 Graph, theta 66 Graph, toroidal 117 Graph, total 82 Graph, totally disconnected 16 Graph, trivial 9 Graph, unicyclic 41 Graph, uniquely colorable 137 Graphoid 41 Group 160 Group of a graph 161 Group, color graph of 168 Group, configuration 181 Group, exponentiation 177 Group, pair 185 Group, permutation 161 Group, power 164 Hamiltonian cycle 65 Hamiltonian graph 65 Hereditary property 96 Homeomorphic graphs 107 Homomorphism 143 Homomorphism, complete of order n 143 Homomorphism, elementary 143 Identical permutation groups 161 Identity graph 161 In-tree 201 Incidence, in a digraph 198 Incidence, in a graph 9 Incidence, matrix 152 Indegree 198 Independent points 95 Independent points, lines 86 Independent points, set 40 Independent points, set of lines 95 Independent points, unit entries 53 Induced subgraph 11 Infinite graph 16 Intersection graph 19 Intersection number 19 Interval graph 20 Invariant 11 Irreducible graph 99 Isolated point 15 Isomorphic, graphs 10 Isomorphic, groups 161 Join 21 Joins 9 Labeled graph 10 Length, in a digraph 199 Length, in a graph 13 Line digraph 209 Line disjoint paths 47 Line graph 71 73 Line graph, iterated 133 Line, addition of 11 Line, cover 94 Line, covering number 94 Line, critical (cover) 97 Line, directed 198 Line, independence number 95 Line, of a graph 9 Line, of a matrix 53 Line, ramsey number 82 Line, removal of 11 Line, symmetry 189 Line-chromatic number 133 Line-coloring 133 Line-connectivity 43 Line-core 98 Line-covering number 94 Line-critical graph (color) 142 Line-critical graph (cover) 98 Line-group 161 Line-regular graph 171 Line-symmetric graph 171 Linear subgraph 151 lines, Multiple 10 Loop 10 Map, edge-rooted plane 193 Map, plane 103 Matching, maximum 96 Matching, unaugmentable 96 Matrix, adjacency, of a digraph 151 202 Matrix, adjacency, of a graph 150 Matrix, cocycle 155 Matrix, cycle 154 Matrix, degree 152 Matrix, detour 203 Matrix, distance 206 Matrix, incidence 152
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