## Abstract

Let us denoted the topological connectivity of a simplicial complex C plus 2 by η(C). Let ψ be a function from class of graphs to the set of positive integers together with ∞. Suppose ψ satisfies the following properties: (formula presented) (where G − e is obtained from G by the removal of the edge e), and ψ(G − N({x, y})) ≥ ψ(G) − 1 η(I (G)) ≥ ψ(G) (where (G − N({x, y})) is obtained from G by the removal of all neighbors of x and y (including, of course, x and y themselves). Let us denoted the maximal function satisfying the conditions above by ψ_{0}. Berger [3] prove the following conjecture: η(I (G)) = ψ_{0} (G) for trees and completements of chordal graphs. Kawamura [2] proved conjecture, for chordal graphs. Berger [3] proved Conjecture for trees and completements of chordal graphs. In this article I proved the following theorem: Let G be a circular-arc graph G if ψ_{0} (G) ≤ 2 then η(I (G)) ≤ 2. Prior the attempt to verify the previously mentioned cases, we need a few preparations which will be discussed in the introduction.

Original language | English |
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Pages (from-to) | 159-169 |

Number of pages | 11 |

Journal | Universal Journal of Mathematics and Applications |

Volume | 2 |

Issue number | 4 |

DOIs | |

State | Published - 26 Dec 2019 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2019, Emrah Evren KARA. All rights reserved.

## Keywords

- Circular-Arc Graphs
- Independence Complex
- Topological Connectivity