In 1968, Cohen presented competition graphs in connection with the study of ecological systems. Recently, Cho, Kim and Nam introduced a generalization called the m-step competition graph. In this… (More)

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the main… (More)

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups with automorphism group a p-group. Yet the goal of this… (More)

Let Γ be a quiver on n vertices v1, v2, . . . , vn with gij edges between vi and vj , and let α ∈ Nn. Hua gave a formula for AΓ(α, q), the number of isomorphism classes of absolutely indecomposable… (More)

There is a connection between the expansion of a graph and the eigengap (or spectral gap) of the normalized adjacency matrix (that is, the gap between the first and second largest eigenvalues).… (More)

In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like “pegging moves” allowed. Motivated by well-studied questions in graph pebbling, we… (More)

This report is a survey of self-dual binary codes. We present the fundamental MacWilliams identity and Gleason’s theorem on self-dual binary codes. We also examine the upper bound of minimum weights… (More)

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of… (More)

This survey on the automorphism groups of finite p-groups focuses on three major topics: explicit computations for familiar finite p-groups, such as the extraspecial p-groups and Sylow p-subgroups of… (More)