C. Mynhardt

activity

20152020

most citedBroadcasts in Graphs: Diametrical Trees

5 citations · 11 across the 7 of their papers we have counts for

collaborators

10 papers

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

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

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 $f (u) = 2$ …

cs.DM2018

The $k$ -conversion number of regular graphs

C. M. Mynhardt, J. L. Wodlinger

Given a graph $G = (V, E)$ and a set $S_{0} \subseteq V$ , an irreversible $k$ -threshold conversion process on $G$ is an iterative process wherein, for each $t = 1, 2, \dots$ , $S_{t}$ is obtain…

math.CO2017★ 1 cited

On k-Total Dominating Graphs

Saeid Alikhani, Davood Fatehi, Kieka Mynhardt

For a graph G, the k-total dominating graph D_{k}^{t}(G) is the graph whose vertices correspond to the total dominating sets of G that have cardinality at most k; two vertices of D…