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Tutte W.T. Ч Connectivity in Graphs
Tutte W.T. Ч Connectivity in Graphs

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Ќазвание: Connectivity in Graphs

јвтор: Tutte W.T.


In mathematics, a graph is a representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.

язык: en

–убрика: ћатематика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1966

 оличество страниц: 155

ƒобавлена в каталог: 10.02.2013

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
ѕредметный указатель
$\theta$-graph      130 134
1-joining of vertices      72
2-connection      114Ч126
2-connection and nodal 2-connection      131
2-connection and non-separability      97Ч98
2-connection modulo [x,y]      114Ч116
3-bond, infinite connectivity of      99
3-connection      104Ч113
3-connection and hinges      119
3-connection of wheels      103
3-connection, classification of graphs with      111Ч113 140
3-connection, classification of trivalent graphs with      140
3-connection, recognition of      137Ч138
ARC      22Ч26
Arc and simple path      30
Arc, adjunction of      133Ч136
Arc, and nodal 2-connection      129Ч130
Arc, automorphism group of      54
Arc, end of      22
Arc, internal vertex of      22
Arc, part of      24
Arcs, internally disjoint      26
Automorphism group of 2-cage and 3-cage      72
Automorphism group of arc      54
Automorphism group of polygon      54
Automorphism group of Thomsen graph      71
Automorphism group of wheel      102Ч103
Automorphism of graphs      52Ч64
Automorphism of graphs, trivial      52
Avoidance of subgraph by arc      23Ч24
Betti number of dimension 0      13Ч14 18
Betti number of dimension 1      18
Bipartition      67
Blocking of semi-simple path      30
Blocking of semi-simple path in Euler graph      36
BOND      98
Bond as cleavage unit      125
Bond, absence of hinges in      119
Branch      127Ч128
Branch, isolated      127
Branch-graph      128
Branch-graph and 3-connection      102
Branch-graph, cage      65 72Ч81
Circuit      30
Circuit, Euler      36 41Ч42
Cleavage      120Ч126
Cleavage graph      120
Cleavage graph and augmented graph      121Ч126
Cleavage graph, hinges in      121
Cleavage units      124Ч126
Cleavage units, determination of      137Ч138
Cleavage units, tree of      125Ч126
CLIQUE      3 70
Clique, 3-connection of      102
Complement of subgraph      8
Component      13
Component and contractive mapping      45Ч46
Component modulo a subgraph      11Ч13 23Ч26 133
Component modulo a subgraph and separation      84
Component modulo a subgraph in arc      22Ч23
Component modulo a subgraph in polygon      27
Component modulo a subgraph in tree      20
Component modulo a subgraph, determination of      35
Component modulo a subgraph, inner      35
Component modulo a subgraph, outer      35
Component modulo a subgraph, Y-graph in      26
Connected graphs, classification of      49Ч50
Connection      13
Connection and 1-connection      97
Connection and spanning trees      21
Connection modulo a subgraph      9Ч16 84
Connection modulo a subgraph and arcs      23Ч25
Connection of graph determined by path      28
Connectivity      97Ч99
Connectivity and symmetry      101Ч103
Connectivity, infinite      97Ч99
Cremona Ч Richmond configuration, and 8-cage      77
cube      4 72
Cut-forest      90Ч92
Cut-vertex      89
Cyclic connection      95Ч96
Cyclic connection and cyclic elements      96
Cyclic element      86Ч92
Cyclic element, characterization of      88Ч89
Cyclic element, terminal      92
Detachment      9Ч10
Diameter      65
Distance modulo a subgraph      32Ч35
Distance of vertex from subgraph      65Ч67
Distance of vertex from vertex      35
dodecahedron      4 72
EDGE      3
Edge, contraction of, and connectivity      104
Edge, deletion of, and connectivity      103Ч104
Edge, end of      3
Edge, essential      104Ч106 110Ч111
Edge, subdivision of      140Ч141
Edge, virtual      120Ч126
Euler      36Ч42
Euler, inverse of      28
Euler, isthmus-avoiding      40Ч42
Euler, length of      28
Euler, origin of      28
Euler, re-entrant      29 36 38
Euler, semi-simple      29Ч30
Euler, simple      30Ч31
Euler, terminus of      28
Euler, vertex-term of      28
Excisable [x,y]-component      118 120Ч121
Flag      99Ч101
Forest      17 18
Forest and arbitrarily traceable graph      39
Forest and polygon      27
Girth and distance      68Ч70
Girth and s-transitivity      61Ч62
Girth and valency      70Ч83
Graph      3
Graph, abstract      48Ч50
Graph, arbitrarily traceable      38Ч39
Graph, augmented      121Ч124
Graph, bipartite      67Ч68 70Ч71
Graph, Euler      36
Graph, exterior, in cage      72
Graph, k-separated      97
Graph, regular      54 69Ч83
Graph, s-regular      62Ч64
Graph, s-transitive      59Ч64
Graph, separable      84
Graph, simple      50 98 101
Graph, symmetrical      52
Graph, wings in augmented      122Ч126
Group      52Ч53
Group, dihedral      54
Group, order of      52
Group, symmetric      54
Heawood graph      60Ч62
Heawood graph as 6-cage      74
Hinge      118Ч121
Hinge, determination of      138
Hinge-component      118Ч119
Homeomorphism and nodal connectivity      132
Homeomorphism and subdivision      140Ч141
Homeomorphism of graphs      131Ч133
incidence      3
Inverse of homeomorphism      132
Inverse of mapping      44Ч45
Inverse of path      28
Isomorphism of arcs      47
Isomorphism of graphs      46Ч47
Isomorphism of groups      53
Isomorphism of polygons      47
Isomorphism, class of graphs      46Ч47
Isthmus      17
Isthmus and connectivity      98
Isthmus and cyclic element      87
Isthmus and Euler graph      40
Isthmus and polygon      27
Isthmus in non-separable graph      84
Isthmus, end-graph of      17 20 23
Isthmus, valencies in end-graph of      40
Joining of vertices by arc      22
Joining of vertices by edge      3
Length of arc      31
Length of path      28
Length of recessional sequence      33
Link      3
Link-graph      3
Link-graph as 1-bond      98
Link-graph, infinite connectivity of      99
Link-graph, non-separability of      84
Loop      3
Loop and connectivity      98
Loop and cyclic element      87
Loop and Euler path      42
Loop in non-separable graph      84
Loop-graph      3
Loop-graph as polygon      26
Loop-graph, infinite connectivity of      99
Loop-graph, non-separability of      84
Lune      26
Lune as 2-bond      98
Lune, infinite connectivity of      99
Mapping of graphs      43Ч47 116Ч118
Mapping of graphs, contractive      45Ч46 92Ч95
Mapping of graphs, identical      46
Mapping of graphs, inverse of      44Ч45
Mcgee graph as 7-cage      77Ч81
Mcgee graph, 3-connection of      102
Multiplicity of vertex in path      29
n-bond      98
n-connection      97
Nodal 2-connection      129Ч131
Nodal 2-connection and 2-connection      131
Nodal 3-connection      134Ч136
Nodal 3-connection, classification of graphs with      138Ч140
Nodal connectivity      129Ч130
Nodal connectivity and homeomorphism      132
Nodal k-separation      129
Nodal k-separation and k-separation      130Ч131
Nodal n-connection      129Ч130
Nodal n-connection and n-connection      129
Nodal subgraph      128Ч129
Nodal subgraph and homeomorphism      132
Node      127Ч128
Non-separable graphs      84Ч86 94Ч95
Non-separable graphs and loop or isthmus      84
Non-separable graphs, 2-connection of      97
Non-separable graphs, classification of      85Ч86
Non-separable graphs, connection of      84
Null graph      3
Null graph, advancing      56Ч59
Null graph, circular      30Ч32
Null graph, degenerate      28
Null graph, edge-term of      28
Null graph, infinite connectivity of      99
Null graph, non-separability of      84
Null graph, path      28Ч35
Paths, product of      29
Petersen graph      74
Polygon      26Ч27
Polygon and arbitrarily traceable graph      38Ч39
Polygon and bipartite graph      68
Polygon and circular path      30Ч32
Polygon and isolated branch      127Ч128
Polygon and isthmus      27
Polygon and nodal 2-connection      130
Polygon as cleavage unit      125
Polygon in Euler graph      36
Polygon, absence of hinges in      119Ч120
Polygon, automorphism group of      54
Polygon, even      68
Polygon, non-separability of      85
Polygon, odd      68
Polygon, residual arcs in      27
Polygon, sense of description of      32
Product of homeomorphisms      132
Product of homeomorphisms of mappings      43
Product of homeomorphisms of paths      28Ч29
Product of homeomorphisms, recessional sequence      33
Reduction      5
Reduction, cyclic element as      87
Representative graph of subgraph-pair      14Ч15
Robertson graph      72 (footnote)
Rotation of re-entrant path      29
s-route      56 58Ч64
Separation      84Ч96
Subgraph      5Ч6
Subgraph, cyclically complete      87Ч88
Subgraph, detached      13
Subgraph, generated by vertex-set      5
Subgraph, maximal and minimal      9
Subgraph, proper      5
Subgraph, spanning      5
Subgraphs, disjoint      6
Subgraphs, intersection of      6
Subgraphs, union of      6
Subpath      29
Successor of s-route      58Ч60 62Ч63
Supergraph      5
Supergraph, proper      5
Thomsen graph      71 112
Tracing a graph      36 37Ч42
Tracing a path      36
Transitivity on edges      55Ч56
Transitivity on vertices      55Ч56
TREE      17Ч21
Tree of cleavage units      125Ч126
Tree, spanning      21
Trees, classification of      48Ч49
Trees, s-transitive      59
Triad in 3-connected graph      105Ч110
triangle      26
Triangle in 3-connected graph      105Ч110
Triangle, infinite connectivity of      99
Valency      4Ч5 19
Valency and connectivity      98
Valency and transitivity      59Ч60
Valency in subgraphs of Euler graphs      36
Valency of regular graph      54
Vertex      3
Vertex of attachment      6Ч7 91 93Ч94
Vertex, filling of, by semi-simple path      30
Vertex, isolated      4 87
Vertex-graph      3
Vertex-graph as cyclic element      87
Vertex-graph, infinite connectivity of      99
Vertex-graph, non-separability of      84
Vertices, adjacent      3
Wheel      102Ч103
Wheel and classification of 3-connected graphs      112
Wheel in theory of essential edges      110Ч111
Wing in augmented graph      122Ч126
Y-graph      25Ч26
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