In this paper we consider 3-dimensional generic bar-and-joint realizations of squares of graphs. These graphs are also called molecular graphs due to their importance in the study...
A graph is said to be representable modulo n if its vertices can be labelled with distinct integers between 0 and n - 1 inclusive such that two vertices are adjacent if and only i...
We study the properties of affine rigidity of a (hyper)graph and prove a variety of fundamental results. First, we show that affine rigidity is a generic property (i.e., only depen...
Steven J. Gortler, Craig Gotsman, Ligang Liu, Dyla...
Two types of robust cycle bases are defined via recursively nice arrangements; complete and bipartite complete graphs are shown to have such bases. It is shown that a diagram in a...
Let G = (V, E) be an undirected graph. Let C be a subset of vertices that we shall call a code. For any vertex v V , the neighbouring set N(v, C) is the set of vertices of C at d...