In 1956, Nordhaus and Gaddum gave lower and upper bounds on the sum and the product
of the chromatic number of a graph and its complement, in terms of the order of the graph …

Graphs measure interactions between objects such as friendship links on Twitter,
transactions between Bitcoin users, and the flow of energy in a food chain. While graphs …

Mobile guards on the vertices of a graph are used to defend it against attacks on either its
vertices or its edges. Various models for this problem have been proposed. In this survey we …

Results are presented on the eternal domination problem: defending a graph from an infinite
sequence of attacks, so that each attack is defended by a guard at most distance one from …

A secure (total) dominating set of a graph G=(V, E) is a (total) dominating set X⊆ V with the
property that for each u∈ VX, there exists x∈ X adjacent to u such that (Xx)∪u is (total) …

Robust control theory has been successfully applied to numerous real-world problems using
a small set of devices called controllers. However, the real systems represented by networks …

The eternal domination number of a graph is the number of guards needed at vertices of the
graph to defend the graph against any sequence of attacks at vertices. We consider the …

Mobile guards on the vertices of a graph are used to defend it against an infinite sequence
of attacks on either its vertices or its edges. If attacks occur at vertices, this is known at the …

In the eternal dominating set problem, guards form a dominating set on a graph and at each
step, a vertex is attacked. After each attack, if the guards can “move” to form a dominating set …

This paper surveys the similarities and differences between the game of cops and robbers
and classes of related games. The game of cops and robbers is a class of pursuit–evasion …