C. Mynhardt

activity

20142025

most citedDominating and Irredundant Broadcasts in Graphs

12 citations · 34 across the 13 of their papers we have counts for

collaborators

15 papers

math.CO2025

Bounding the Eviction Number of a Graph in Terms of its Independence Number

Gary MacGillivray, Christina Mynhardt, Virgelot Virgile

An eternal dominating family of graph $G$ in the eviction game is a collection $D_{k} = {D_{1}, ..., D_{l}}$ of dominating sets of $G$ such that (a) $∣ D_{i} ∣ = ∣ D_{j} ∣$ for a…

math.CO2020

Enumerating the Digitally Convex Sets of Powers of Cycles and Cartesian Products of Paths and Complete Graphs

MacKenzie Carr, Christina M. Mynhardt, Ortrud R. Oellermann

Given a finite set $V$ , a convexity $C$ , is a collection of subsets of $V$ that contains both the empty set and the set $V$ and is closed under intersections. The element…

math.CO2020★ 6 cited

Reconfiguration of Colourings and Dominating Sets in Graphs: a Survey

C. M. Mynhardt, S. Nasserasr

We survey results concerning reconfigurations of colourings and dominating sets in graphs. The vertices of the $k$ -colouring graph $C_{k} (G)$ of a graph $G$ correspond to…

math.CO2020★ 1 cited

Total Roman Domination Edge-Supercritical and Edge-Removal-Supercritical Graphs

C. M. Mynhardt, S. E. A. Ogden

A total Roman dominating function on a graph $G$ is a function $f : V (G) \to {0, 1, 2}$ such that every vertex $v$ with $f (v) = 0$ is adjacent to some vertex $u$ with $f (u) = 2$ ,…

math.CO2019★ 3 cited

Total Roman Domination Edge-Critical Graphs

C. Lampman, C. M. Mynhardt, S. E. A. Ogden

A total Roman dominating function on a graph $G$ is a function such that every vertex $v$ with $f (v) = 0$ is adjacent to some vertex $u$ with $f (u) = 2$ …

math.CO2019★ 2 cited

Boundary Independent Broadcasts in Graphs

Christina Mynhardt, Linda Neilson

A broadcast on a nontrivial connected graph G is a function f from the vertices of G to the non-negative integers such that f(v) does not exceed e(v) (the eccentricity of v) for ea…