Vol 19 no. 1

1. A characterization of trees with equal 2-domination and 2-independence numbers

Brause, Christoph ; Henning, Michael A. ; Krzywkowski, Marcin.
A set $S$ of vertices in a graph $G$ is a $2$-dominating set if every vertex of $G$ not in $S$ is adjacent to at least two vertices in $S$, and $S$ is a $2$-independent set if every vertex in $S$ is adjacent to at most one vertex of $S$. The $2$-domination number $\gamma_2(G)$ is the minimum […]
Section: Graph Theory

2. A New Game Invariant of Graphs: the Game Distinguishing Number

Gravier, Sylvain ; Meslem, Kahina ; Schmidt, Simon ; Slimani, Souad.
The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring. A distinguishing $d$-coloring is a coloring […]
Section: Graph Theory

3. Postorder Preimages

Defant, Colin.
Given a set $Y$ of decreasing plane trees and a permutation $\pi$, how many trees in $Y$ have $\pi$ as their postorder? Using combinatorial and geometric constructions, we provide a method for answering this question for certain sets $Y$ and all permutations $\pi$. We then provide applications of […]
Section: Combinatorics

4. The Existence of Planar Hypotraceable Oriented Graphs

van Aardt, Susan,  ; Burger, Alewyn Petrus ; Frick, Marietjie.
A digraph is \emph{traceable} if it has a path that visits every vertex. A digraph $D$ is \emph{hypotraceable} if $D$ is not traceable but $D-v$ is traceable for every vertex $v\in V(D)$. It is known that there exists a planar hypotraceable digraph of order $n$ for every $n\geq 7$, but no examples […]
Section: Graph Theory

5. A class of symmetric difference-closed sets related to commuting involutions

Campbell, John.
Recent research on the combinatorics of finite sets has explored the structure of symmetric difference-closed sets, and recent research in combinatorial group theory has concerned the enumeration of commuting involutions in $S_{n}$ and $A_{n}$. In this article, we consider an interesting combination […]
Section: Combinatorics