Minimal line graphs

@article{Sumner1976MinimalLG,
  title={Minimal line graphs},
  author={David P. Sumner},
  journal={Glasgow Mathematical Journal},
  year={1976},
  volume={17},
  pages={12-16}
}
  • D. Sumner
  • Published 1976
  • Mathematics
  • Glasgow Mathematical Journal
In this paper all graphs will be ordinary graphs, i.e. finite, undirected, and without loops or multiple edges. For points x and y of a graph G , we shall indicate that x is adjacent to y by writing x ⊥ y , and if x is not adjacent to y we shall write x y . We shall denote the degree of a point x by δ( x ) and the minimal degree of G by δ( G ). By the line graph of a graph G we shall mean the graph L ( G ) whose points are the edges of G , with two points of L ( G ) adjacent whenever they are… Expand
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Let G be a finite graph. The interchange graph G' of G, has a vertex corresponding to each edge of G, two vertices of G' being connected if the corresponding edges of G have a common vertex in G. InExpand
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Abstract The derived graph of a graph G has the edges of G as its vertices, with adjacency determined by the adjacency of the edges in G . A new characterization of derived graphs is given in termsExpand
Graph theory