Abstract--This paper considers a second-order consensus problem for multiagent systems with nonlinear dynamics and directed topologies where each agent is governed by both position...
: TGraphs are directed graphs with typed, attributed, and ordered nodes and edges. These properties leverage the use of graphs as models for all kinds of artifacts in the context o...
The domatic number of a graph G is the maximum number of dominating sets into which the vertex set of G can be partitioned. We show that the domatic number of a random r-regular g...
In [5], Reed conjectures that every graph satisfies ++1 2 . We prove this holds for graphs with disconnected complement. Combining this fact with a result of Molloy proves the co...
We establish that every cyclically 4-connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp and we present all nonhamil...
Robert E. L. Aldred, S. Bau, Derek A. Holton, Bren...