12 citations · 15 across the 5 of their papers we have counts for
6 papers
Irredundance Trees of Diameter 3
C. M. Mynhardt, A. Roux
A set D of vertices of a graph G with vertex set V is irredundant if each non-isolated vertex of G[D] has a neighbour in V-D that is not adjacent to any other vertex in D. The uppe…
The Localization Game On Cartesian Products
Jeandré Boshoff, Adriana Roux
The localization game is played by two players: a Cop with a team of cops, and a Robber. The game is initialised by the Robber choosing a vertex , unknown to the Cop.…
Critical graphs upon multiple edge subdivision
Magda Dettlaff, Magdalena Lemanska, Adriana Roux
A subset of is \emph{dominating} in if every vertex of has at least one neighbour in let be the minimum cardinality among all dominating sets in …
Irredundance Graphs
Kieka Mynhardt, Riana Roux
A set D of vertices of a graph G=(V,E) is irredundant if each v of D satisfies (a) v is isolated in the subgraph induced by D, or (b) v is adjacent to a vertex in V-D that is nonad…
Connected k-Dominating Graphs
C. M. Mynhardt, R. Roux, L. E. Teshima
For a graph G=(V,E), the k-dominating graph of G, denoted by , has vertices corresponding to the dominating sets of G having cardinality at most k, where two vertices of…
Dominating and Irredundant Broadcasts in Graphs
Kieka Mynhardt, Riana Roux
A broadcast on a nontrivial connected graph G=(V,E) is a function f from V(G) to {0,1,...,diam(G)} such that f(v) does not exceed the eccentricity of v. The cost of f is the sum of…