On 2-arc-transitive graphs of product action type

In this paper, we discuss the structural information about 2-arc-transitive (non-bipartite and bipartite) graphs of product action type. It is proved that a 2-arc-transitive graph of product action type requires certain restrictions on either the vertex-stabilizers or the valency. Based on the existence of some equidistant linear codes, a construction is given for 2-arc-transitive graphs of non-diagonal product action type, which produces several families of such graphs. Besides, a nontrivial construction is given for 2-arc-transitive bipartite graphs of diagonal product action typeComment: 18 page

Cubic s-arc transitive Cayley graphs

AbstractThis paper gives a characterization of connected cubic s-transitive Cayley graphs. It is shown that, for s≥3, every connected cubic s-transitive Cayley graph is a normal cover of one of 13 graphs: three 3-transitive graphs, four 4-transitive graphs and six 5-transitive graphs. Moreover, the argument in this paper also gives another proof for a well-known result which says that all connected cubic arc-transitive Cayley graphs of finite non-abelian simple groups are normal except two 5-transitive Cayley graphs of the alternating group A47

Tetravalent edge-transitive Cayley graphs with odd number of vertices

AbstractA characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu [Automorphism groups and isomorphisms of Cayley graphs, Discrete Math. 182 (1998) 309–319] regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of half-transitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a ‘nice’ isomorphic 2-factorisation

TETRAVALENT EDGE-TRANSITIVE CAYLEY GRAPHS WITH ODD NUMBER OF VERTICES

Abstract. A characterisation is given of edge-transitive Cayley graphs of valency 4 on odd number of vertices. The characterisation is then applied to solve several problems in the area of edge-transitive graphs: answering a question proposed by Xu (1998) regarding normal Cayley graphs; providing a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex-stabiliser; constructing and characterising a new family of halftransitive graphs. Also this study leads to a construction of the first family of arc-transitive graphs of valency 4 which are non-Cayley graphs and have a 'nice' isomorphic 2-factorisation

Enhanced inhibition of Avian leukosis virus subgroup J replication by multi-target miRNAs

<p>Abstract</p> <p>Background</p> <p>Avian leukosis virus (ALV) is a major infectious disease that impacts the poultry industry worldwide. Despite intensive efforts, no effective vaccine has been developed against ALV because of mutations that lead to resistant forms. Therefore, there is a dire need to develop antiviral agents for the treatment of ALV infections and RNA interference (RNAi) is considered an effective antiviral strategy.</p> <p>Results</p> <p>In this study, the avian leukosis virus subgroup J (ALV-J) proviral genome, including the <it>gag </it>genes, were treated as targets for RNAi. Four pairs of miRNA sequences were designed and synthesized that targeted different regions of the <it>gag </it>gene. The screened target (i.e., the <it>gag </it>genes) was shown to effectively suppress the replication of ALV-J by 19.0-77.3%. To avoid the generation of escape variants during virus infection, expression vectors of multi-target miRNAs were constructed using the multi-target serial strategy (against different regions of the <it>gag</it>, <it>pol</it>, and <it>env </it>genes). Multi-target miRNAs were shown to play a synergistic role in the inhibition of ALV-J replication, with an inhibition efficiency of viral replication ranging from 85.0-91.2%.</p> <p>Conclusion</p> <p>The strategy of multi-target miRNAs might be an effective method for inhibiting ALV replication and the acquisition of resistant mutations.</p

On basic 22-arc-transitive graphs

A connected graph $\Gamma=(V,E)$ of valency at least $3$ is called a basic $2$-arc-transitive graph if its full automorphism group has a subgroup $G$ with the following properties: (i) $G$ acts transitively on the set of $2$-arcs of $\Gamma$, and (ii) every minimal normal subgroup of $G$ has at most two orbits on $V$. In her papers [17,18], Praeger proved a connected $2$-arc-transitive graph of valency at least $3$ is a normal cover of some basic $2$-arc-transitive graph, and characterized the group-theoretic structures for basic $2$-arc-transitive graphs. Based on Praeger's theorems on $2$-arc-transitive graphs, this paper presents a further understanding on basic $2$-arc-transitive graphs.Comment: 10 page

On primitive permutation groups with small suborbits and their orbital graphs

AbstractIn this paper, we study finite primitive permutation groups with a small suborbit. Based on the classification result of Quirin [Math. Z. 122 (1971) 267] and Wang [Comm. Algebra 20 (1992) 889], we first produce a precise list of primitive permutation groups with a suborbit of length 4. In particular, we show that there exist no examples of such groups with the point stabiliser of order 2436, clarifying an uncertain question (since 1970s). Then we analyse the orbital graphs of primitive permutation groups with a suborbit of length 3 or of length 4. We obtain a complete classification of vertex-primitive arc-transitive graphs of valency 3 and valency 4, and we prove that there exist no vertex-primitive half-arc-transitive graphs of valency less than 10. Finally, we construct vertex-primitive half-arc-transitive graphs of valency 2k for infinitely many integers k, with 14 as the smallest valency