The Mathematics of Chip-firing is a solid introduction and overview of the growing field of
chip-firing. It offers an appreciation for the richness and diversity of the subject. Chip-firing …

Let M denote the Laplacian matrix of a graph G. Associated with G is a finite group Φ (G),
obtained from the Smith normal form of M, and whose order is the number of spanning trees …

We review the status of the two-dimensional Abelian sandpile model as a strong candidate
to provide a lattice realization of logarithmic conformal invariance with a central charge c …

AD Mednykh, IA Mednykh, “Cyclic coverings of graphs. Counting rooted spanning forests and
trees, Kirchhoff index, and Jacobians”, Uspekhi Mat. Nauk, 78:3(471) (2023), 115–164; Russian …

The Jacobian group (also known as the critical group or sandpile group) is an important
invariant of a graph X; it is a finite abelian group whose cardinality is equal to the number of …

The Jacobian group (also known as the critical group or sandpile group) is an important
invariant of a finite, connected graph X; it is a finite abelian group whose cardinality is equal …

The sandpile group of a graph is a refinement of the number of spanning trees of the graph
and is closely connected with the graph Laplacian. In this paper, the structure of the sandpile …

In this article, we study the sandpile group of the cone of a graph. After introducing the
concept of uniform homomorphism of graphs we prove that every surjective uniform …

In this note we introduce a finite abelian group that can be associated with any finite
connected graph. This group can be defined in an elementary combinatorial way in terms of …

We generalize the theory of critical groups from graphs to simplicial complexes. Specifically,
given a simplicial complex, we define a family of abelian groups in terms of combinatorial …