Gerd Fricke

Offensive alliances in graphs

A set S is an offensive alliance if for every vertex v in its boundary N(S)−S it holds that the majority of vertices in v’s closed neighbourhood are in S. The offensive alliance number is the minimum cardinality of an offensive alliance. In this paper we explore the bounds on the offensive alliance and the strong offensive alliance numbers (where a strict majority is required). In particular, we show that the offensive alliance number is at most 2/3 the order and the strong offensive alliance number is at most 5/6 the order.

The Private Neighbor Cube

Let

On the computational complexity of upper fractional domination

S

Reducing the adjacency matrix of a tree

be a set of vertices in a graph

Representations of graphs modulo n

G = (V, E)

γ-graphs of graphs

. The authors state that a vertex u in S has a private neighbor (relative to

On a Nordhaus-Gaddum type problem for independent domination

S

Classes of graphs for which upper fractional domination equals independence, upper domination, and upper irredundance

) if either

Homomorphisms on C(R)

u

On perfect neighborhood sets in graphs

is not adjacent to any vertex in