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Cross-index of a Graph

  • Kawauchi, Akio (Osaka City University Advanced Mathematical Institute) ;
  • Shimizu, Ayaka (Department of Mathematics, National Institute of Technology) ;
  • Yaguchi, Yoshiro (Department of Mathematics, National Institute of Technology)
  • Received : 2018.01.14
  • Accepted : 2019.02.13
  • Published : 2019.12.23

Abstract

For every tree T, we introduce a topological invariant, called the T-cross-index, for connected graphs. The T-cross-index of a graph is a non-negative integer or infinity according to whether T is a tree basis of the graph or not. It is shown how this cross-index is independent of the other topological invariants of connected graphs, such as the Euler characteristic, the crossing number and the genus.

Keywords

Acknowledgement

Supported by : JSPS, The Sumitomo Foundation

The first author was supported by JSPS KAKENHI Grant Number 24244005. The second author was supported by Grant for Basic Science Research Projects from The Sumitomo Foundation (160154).

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