J. Topp

activity

20162024

collaborators

Showing math.COShow all

12 papers · 1 filter

math.CO2024

On total domination subdivision numbers of trees

Michael A. Henning, Jerzy Topp

A set $S$ of vertices in a graph $G$ is a total dominating set of $G$ if every vertex is adjacent to a vertex in $S$ . The total domination number $γ_{t} (G)$ is the minimum cardinalit…

math.CO2022

Characterization of $α$ -excellent $2$ -trees

Magda Dettlaff, Michael A. Henning, Jerzy Topp

A graph is $α$ -excellent if every vertex of the graph is contained in some maximum independent set of the graph. In this paper, we present two characterizations of the $α$ -excellen…

math.CO2021

Minimal graphs with disjoint dominating and total dominating sets

Michael A. Henning, Jerzy Topp

A graph $G$ is a DTDP-graph if it has a pair $(D, T)$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $T$ is a total dominating set of $G$ . Such graphs wer…

math.CO2021

Graphs with disjoint 2-dominating sets

Michael A. Henning, Jerzy Topp

A subset $D \subseteq V_{G}$ is a dominating set of $G$ if every vertex in $V_{G} ∖ D$ has a neighbor in $D$ , while $D$ is a 2-dominating set of $G$ if every vertex belonging to…

math.CO2019

Minimal graphs with disjoint dominating and paired-dominating sets

Michael A. Henning, Jerzy Topp

A subset $D \subseteq V_{G}$ is a dominating set of $G$ if every vertex in $V_{G} - D$ has a~neighbor in $D$ , while $D$ is a paired-dominating set of $G$ if $D$ is a~dominating set and th…

math.CO2019

Disjoint dominating and 2-dominating sets in graphs

Mateusz Miotk, Jerzy Topp, Paweł Żyliński

A graph $G$ is a $D D_{2}$ -graph if it has a pair $(D, D_{2})$ of disjoint sets of vertices of $G$ such that $D$ is a dominating set and $D_{2}$ is a 2-dominating set of $G$ . We provide…

On total domination subdivision numbers of trees

Characterization of α-excellent 2-trees

Minimal graphs with disjoint dominating and total dominating sets

Graphs with disjoint 2-dominating sets

Minimal graphs with disjoint dominating and paired-dominating sets

Disjoint dominating and 2-dominating sets in graphs

Characterization of $α$ -excellent $2$ -trees