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The number of empty neighbors of a cluster.

A sum over all cluster perimeters.

Erdős and Rényi (1960) showed that for many monotone-increasing properties of random graphs, graphs of a size slightly less than a certain threshold are very unlikely to have ...

There are at least two distinct notions of when a point process is stationary. The most commonly utilized terminology is as follows: Intuitively, a point process X defined on ...

The scramble number sn(G) of a graph G is a graph invariant developed to aid in the study of gonality of graphs. The scramble number is NP-hard to compute (Echavarria et al. ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

A distinct (including reflections and rotations) arrangement of adjacent squares on a grid, also called a fixed polyomino.

The gonality (also called divisorial gonality) gon(G) of a (finite) graph G is the minimum degree of a rank 1 divisor on that graph. It can be thought of as the minimum ...

Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll. The ...

A Cayley tree is a tree in which each non-leaf graph vertex has a constant number of branches n is called an n-Cayley tree. 2-Cayley trees are path graphs. The unique ...