## Graph theory and applications |

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### Contents

Authors Preface | 9 |

The notion of the connectivity of a graph and some attempts | 20 |

Some problems involving weighted graphs | 27 |

Copyright | |

8 other sections not shown

### Common terms and phrases

acyclic orientations applied arrows articulation points calculation chord chromatic polynomial cluster integral coloured alike complete graph conductors configurations connected graphs consider corresponding cyclomatic number define deletion-contraction algorithm directed cycle directed graph disconnecting set domains dual graph dual lattice edges eigenvalues enumeration problems equation Euler circuits exactly example expected number factor four points generalisation graph containing graph theory independent interactions isolated point known large number lines incident lines joining mathematical matrix molecules neighbours node number of lines number of points obtained Onsager-Ising operation original graph pair of points partition function path Pfaffian planar graphs plane square lattice polygon possible colourings Potts model Potts problem recurrence relation result series expansions series-parallel series-parallel graphs set of lines shown in Fig simple sling statistical mechanics step subgraph Temperley theorem transformation tree-generating determinant valency variables various vertex vertices virial coefficients voltage weight winning situation zero