In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

Characterizing regular covers of symmetric graphs is one the fundamental topics in field algebraic graph theory, and often a key step for approaching general graphs. Complete graphs, which are typical naturally appear study many as normal quotient In this paper, characterization edge-transitive cyclic complete with prime power order given by using techniques finite group theory related properti...

Let Γ be a graph admitting an arc-transitive subgroup G of automorphisms that leaves invariant a vertex partition B with parts of size v ≥ 3. In this paper we study such graphs where: for B, C ∈ B connected by some edge of Γ , exactly two vertices of B lie on no edge with a vertex of C; and as C runs over all parts of B connected to B these vertex pairs (ignoring multiplicities) form a cycle. W...

In this paper, we examine the structure of vertexand edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using the Classification of Finite Simple Groups) that no graph in this family has a holomorphic simple automorphism group. We also find some constraints on the parame...

Knödel graphs and Fibonacci graphs are two classes of bipartite incident-graph of circulant digraphs. Both graphs have been extensively studied for the purpose of fast communications in networks, and they have deserved a lot of attention in this context. In this paper, we show that there exists an O(n log n)-time algorithm to recognize Knödel graphs, and that the same technique applies to Fibon...

For a graph Γ, subgroups M < G 6 Aut(Γ), and an edge partition E of Γ, the pair (Γ, E) is a (G, M)-homogeneous factorisation if M is vertex-transitive on Γ and fixes setwise each part of E , while G permutes the parts of E transitively. A classification is given of all homogeneous factorisations of finite Johnson graphs. There are three infinite families and nine sporadic examples.

Implication graphs are used to solve the test generation, redundancy identification, synthesis, and verification problems of digital circuits. We propose a new “oring” node structure to represent partial implications in a graph. The oring node is the contrapositive of the previously used “anding” node. The addition of a single oring node in the implication graph of a Boolean gate eliminates the...

A graph is half-arc-transitive if its automorphism group acts transitively on vertices and edges, but not on arcs. Let p be a prime. Cheng and Oxley [On weakly symmetric graphs of order twice a prime, J. Combin. Theory B 42(1987) 196-211] proved that there is no half-arc-transitive graph of order 2p, and Alspach and Xu [ 12 -transitive graphs of order 3p, J. Algebraic Combin. 3(1994) 347-355] c...