## Connectivity in graphs |

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### Contents

GRAPHS AND SUBGRAPHS | 3 |

CONNECTION MODULO A SUBGRAPH | 9 |

TREES ARCS AND POLYGONS | 17 |

Copyright | |

10 other sections not shown

### Common terms and phrases

1-joined 3-connected adjacent advancing path automorphism ax(G bipartite blocked semi-simple path branch of G circular path cleavage units complement component of G connected graph construct contractive mapping cyclic element deduce definition denote distinct vertices divalent edge of G edge or vertex edge-term element of G Euler path Fx n F2 G is connected girth graph G H. S. M. Coxeter Heawood graph Hence G homeomorphism incident isomorphism joined Let G Let H link-graph loop loop-graph Math McGee graph monovalent terminus monovalent vertex Moreover nodal subgraph nodally 3-connected non-null subgraph non-separable graph null graph path in G polygon positive integer Proof proper subgraph regular graph s-transitive simple path subgraph H subgraph of G Suppose G theorem follows transitive traverses tree trivial val(G valency vertex-graph vertex-term vertices of attachment vertices of G virtual edge W. T. Tutte write x e V(H x]-component