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On the ideal triangulation graph of a punctured surface

Mustafa Korkmaz, Athanase Papadopoulos (2012)

Annales de l’institut Fourier

We study the ideal triangulation graph T ( S ) of an oriented punctured surface S of finite type. We show that if S is not the sphere with at most three punctures or the torus with one puncture, then the natural map from the extended mapping class group of S into the simplicial automorphism group of T ( S ) is an isomorphism. We also show that the graph T ( S ) of such a surface S , equipped with its natural simplicial metric is not Gromov hyperbolic. We also show that if the triangulation graph of two oriented punctured...

On the index of length four minimal zero-sum sequences

Caixia Shen, Li-meng Xia, Yuanlin Li (2014)

Colloquium Mathematicae

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = ( n g ) · . . . · ( n l g ) where g ∈ G and n , . . . , n l i [ 1 , o r d ( g ) ] , and the index ind(S) is defined to be the minimum of ( n + + n l ) / o r d ( g ) over all possible g ∈ G such that ⟨g⟩ = G. A conjecture says that every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. This conjecture was confirmed recently for the case when |G| is a product of at most two prime powers. However, the general case is still open. In this paper, we make some...

On the intersection graph of a finite group

Hossein Shahsavari, Behrooz Khosravi (2017)

Czechoslovak Mathematical Journal

For a finite group G , the intersection graph of G which is denoted by Γ ( G ) is an undirected graph such that its vertices are all nontrivial proper subgroups of G and two distinct vertices H and K are adjacent when H K 1 . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of Aut ( Γ ( G ) ) .

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