6 citations · 13 across the 9 of their papers we have counts for
10 papers
On fixing and distinguishing numbers of trees
Calum Buchanan, Peter Dankelmann, Isabel Harris +3
A graph is -distinguishable if there is a labeling of its vertices with labels such that the only automorphism of which preserves the labeling is the identity. The d…
Paint cost spectrum of perfect -ary trees
Sonwabile Mafunda, Jonathan L. Merzel, K. E. Perry +1
We determine the paint cost spectrum for perfect -ary trees. A coloring of the vertices of a graph with colors is said to be \emph{-distinguishing} if only the trivia…
Toughness of recursively partitionable graphs
Calum Buchanan, Brandon Du Preez, K. E. Perry +1
A simple graph on vertices is said to be recursively partitionable (RP) if , or if is connected and satisfies the following recursive property: for…
Symmetry Parameters for Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
The Mycielskian construction, denoted , takes a finite simple graph to a larger graph with of the same clique number but larger chromatic number. The generalized Mycielsk…
An Extremal Problem on Rainbow Spanning Trees in Graphs
Matthew DeVilbiss, Bradley Fain, Amber Holmes +3
A spanning tree of an edge-colored graph is rainbow provided that each of its edges receives a distinct color. In this paper we consider the natural extremal problem of maximizing…
Distinguishing Generalized Mycielskian Graphs
Debra Boutin, Sally Cockburn, Lauren Keough +3
A graph is -distinguishable if there is a coloring of the vertices with colors so that only the trivial automorphism preserves the color classes. The smallest such i…