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Tetravalent Arc-Transitive Graphs of Order 3p 2

Mohsen Ghasemi (2014)

Discussiones Mathematicae Graph Theory

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given

Tetravalent half-arc-transitive graphs of order p 2 q 2

Hailin Liu, Bengong Lou, Bo Ling (2019)

Czechoslovak Mathematical Journal

We classify tetravalent G -half-arc-transitive graphs Γ of order p 2 q 2 , where G 𝖠𝗎𝗍 Γ and p , q are distinct odd primes. This result involves a subclass of tetravalent half-arc-transitive graphs of cube-free order.

The classification of finite groups by using iteration digraphs

Uzma Ahmad, Muqadas Moeen (2016)

Czechoslovak Mathematical Journal

A digraph is associated with a finite group by utilizing the power map f : G G defined by f ( x ) = x k for all x G , where k is a fixed natural number. It is denoted by γ G ( n , k ) . In this paper, the generalized quaternion and 2 -groups are studied. The height structure is discussed for the generalized quaternion. The necessary and sufficient conditions on a power digraph of a 2 -group are determined for a 2 -group to be a generalized quaternion group. Further, the classification of two generated 2 -groups as abelian or non-abelian...

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