Kaishun Wang

s -Regular cyclic coverings of the three-dimensional hypercube Q 3

A graph is s-regular if its automorphism group acts regularly on the set of s-arcs. An infinite family of cubic 1-regular graphs was constructed in European J. Combin. 23 (2002) 559, as cyclic coverings of the three-dimensional hypercube Q3. In this paper, we classify the s-regular cyclic coverings of Q3 for each s ≥ 1, whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.

Metric dimension of some distance-regular graphs

A resolving set of a graph is a set of vertices with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. In this paper, we construct a resolving set of Johnson graphs, doubled Odd graphs, doubled Grassmann graphs and twisted Grassmann graphs, respectively, and obtain the upper bounds on the metric dimension of these graphs.

Association schemes based on attenuated spaces

The subspaces of a given dimension in an attenuated space form the points of an association scheme. If the dimension is maximal, it is the bilinear forms graph, which has been thoroughly studied. In this paper, we discuss the general case, and obtain a family of symmetric association schemes which are a common generalization of the Grassmann schemes and the bilinear forms schemes. Moreover, all the parameters of the association scheme are computed.

Tetravalent half-transitive graphs of order 4p

A graph is half-transitive if its automorphism group acts transitively on its vertex set and edge set, but not on its arc set. In this paper, the tetravalent half-transitive graphs of order 4p are classified for each prime p. It is shown that there are no tetravalent half-transitive Cayley graphs of order 4p and a tetravalent half-transitive non-Cayley graph of order 4p exists if and only if p-1 is divisible by 8, which is unique for a given order.

Singular linear space and its applications

Abstract As a generalization of attenuated spaces, the concept of singular linear spaces was introduced in [K. Wang, J. Guo, F. Li, Association schemes based on attenuated spaces, European J. Combin. 31 (2010) 297–305]. This paper first gives two anzahl theorems in singular linear spaces, and then discusses their applications to the constructions of Deza digraphs, quasi-strongly regular graphs, lattices and authentication codes.

The structure and metric dimension of the power graph of a finite group

The power graph P G of a finite group G is the graph with the vertex set G , where two distinct vertices are adjacent if one is a power of the other. We first show that P G has a transitive orientation, so it is a perfect graph and its core is a complete graph. Then we use the poset on all cyclic subgroups of G (under usual inclusion) to characterize the structure of P G . Finally, a closed formula for the metric dimension of P G is established. As an application, we compute the metric dimension of the power graph of a cyclic group.

The full automorphism group of the power (di)graph of a finite group

We describe the full automorphism group of the power (di)graph of a finite group. As an application, we solve a conjecture proposed by Doostabadi, Erfanian and Jafarzadeh in 2013.

Pooling spaces associated with finite geometry

Motivated by the works of Ngo and Du [H. Ngo, D. Du, A survey on combinatorial group testing algorithms with applications to DNA library screening, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 55 (2000) 171-182], the notion of pooling spaces was introduced [T. Huang, C. Weng, Pooling spaces and non-adaptive pooling designs, Discrete Mathematics 282 (2004) 163-169] for a systematic way of constructing pooling designs; note that geometric lattices are among pooling spaces. This paper attempts to draw possible connections from finite geometry and distance regular graphs to pooling spaces: including the projective spaces, the affine spaces, the attenuated spaces, and a few families of geometric lattices associated with the orbits of subspaces under finite classical groups, and associated with d-bounded distance-regular graphs.

The Rainbow Connection Number of the Power Graph of a Finite Group

This paper studies the rainbow connection number of the power graph