Isoperimetric Constants of ð d ; f Þ-Regular Planar Graphs

  title={Isoperimetric Constants of ð d ; f Þ-Regular Planar Graphs},
  author={H Yusuke and Shirai Tomoyuki},
Let G 1⁄4 ðVðGÞ;EðGÞÞ be a connected undirected graph without loops and multiple edges, where VðGÞ is the set of vertices and EðGÞ is the set of edges. For x 2 VðGÞ, the degree of x in G, denoted by degGðxÞ, implies the number of edges incident with x, and the neighbourhood of x in G, denoted by NGðxÞ, implies the set of vertices adjacent to x in G; thus degGðxÞ 1⁄4 jNGðxÞj. Definitions and notation on graphs which are not given in this note can be found in [1, 2]. A graph G is said to be a ðd… CONTINUE READING

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