Mohsen Ghasemi

Cubic semisymmetric graphs of order 6p3

A regular edge-transitive graph is said to be semisymmetric if it is not vertex-transitive. By Folkman [J. Folkman, Regular line-symmetric graphs, J. Combin Theory 3 (1967) 215-232], there is no semisymmetric graph of order 2p or 2p^2 for a prime p and by Malnic, et al. [A. Malnic, D. Marusic, C.Q. Wang, Cubic edge-transitive graphs of order 2p^3, Discrete Math. 274 (2004) 187-198], there exists a unique cubic semisymmetric graph of order 2p^3, the so-called Gray graph of order 54. In this paper it is shown that a connected cubic semisymmetric graph of order 6p^3 exists if and only if p-1 is divisible by 3. There are exactly two such graphs for a given order, which are constructed explicitly.

Finite groups with two composite character degrees

Let G be a finite group and let cd(G) be the set of all irreducible character degrees of G. We consider finite groups G with the property that cd(G) has at most two composite members. We derive a bound 6 for the size of character degree sets of such groups. There are examples in both solvable and nonsolvable groups where this bound is met. In the case of nonsolvable groups, we are able to determine the structure of such groups with |cd(G)|≤ 6.

Tetravalent arc-transitive graphs of order twice a product of two primes

Abstract In this article a complete classification of tetravalent arc-transitive graphs of order twice a product of two primes is given.

Finite groups with three composite character degrees

ABSTRACT Let G be a finite group and let cd(G) be the set of all irreducible character degrees of G. We consider finite groups G with the property that cd(G) has at most three composite members. We derive a bound 8 for the size of character degree sets of such groups.

Tetravalent Vertex-Transitive Graphs of Order Twice A Prime Square

A graph is vertex-transitive if its automorphism group acts transitively on vertices of the graph. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, a complete classification is given of tetravalent vertex-transitive non-Cayley graphs of order

Tetravalent Arc-Transitive Graphs of Order 3p 2

2p^2

Tetravalent s-Transitive Graphs of Order 4p2

2p2 for any prime p.

Nonsolvable Groups with no Prime Dividing Four Character Degrees

A finite graph is one-regular if its automorphism group acts regularly on the set of its arcs. In the present paper, tetravalent one-regular graphs of order 7p2, where p is a prime, are classified using computer algebra tools.