J. Topp

activity

20132024

most citedOn domination perfect graphs

8 citations · 21 across the 14 of their papers we have counts for

collaborators

17 papers

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.CO2022

On $α$ -excellent graphs

M. Dettlaff, M. A. Henning, J. Topp

A graph $G$ is $α$ -excellent if every vertex of $G$ is contained in some maximum independent set of $G$ . In this paper, we characterize $α$ -excellent bipartite graphs, $α$ -excellen…

math.CO2022

Common domination perfect graphs

Magda Dettlaff, Michael A. Henning, Jerzy Topp

A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex that does not belong to $S$ is adjacent to a vertex in $S$ . The domination number $γ (G)$ of $G$ is t…

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★ 1 cited

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…

math.CO2019★ 1 cited

Bipartization of graphs

Mateusz Miotk, Jerzy Topp, Paweł Żyliński

A dominating set of a graph $G$ is a set $D \subseteq V_{G}$ such that every vertex in $V_{G} - D$ is adjacent to at least one vertex in $D$ , and the domination number $γ (G)$ of $G$ is th…

math.CO2018★ 2 cited

Graphs with equal domination and covering numbers

Andrzej Lingas, Mateusz Miotk, Jerzy Topp +1

A dominating set of a graph $G$ is a set $D \subseteq V_{G}$ such that every vertex in $V_{G} - D$ is adjacent to at least one vertex in $D$ , and the domination number $γ (G)$ of $G$ is th…

math.CO2018★ 8 cited

On domination perfect graphs

Jerzy Topp, Paweł Żyliński

Let $γ (G)$ and $β (G)$ denote the domination number and the covering number of a graph $G$ , respectively. A connected non-trivial graph $G$ is said to be $γ β$ -{perfect} if $γ(H)=β(H…

math.CO2017★ 5 cited

On accurate domination in graphs

Joanna Cyman, Michael A. Henning, Jerzy Topp

A dominating set of a graph $G$ is a subset $D \subseteq V_{G}$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$ . The cardinality of a smallest dominating…

math.CO2017

Graphs with equal domination and certified domination numbers

Magda Dettlaff, Magdalena Lemańska, Mateusz Miotk +3

A set $D$ of vertices of a graph $G$ is a dominating set of $G$ if every vertex in $V_{G} - D$ is adjacent to at least one vertex in $D$ . The domination number (upper domination number…

math.CO2016

Certified domination

Magda Dettlaff, Magdalena Lemańska, Jerzy Topp +2

Imagine that we are given a set $D$ of officials and a set $W$ of civils. For each civil $x \in W$ , there must be an official $v \in D$ that can serve $x$ , and whenever any such $v…

math.CO2016

Coronas and domination subdivision number of a graph

Magda Dettlaff, Magdalena Lemańska, Jerzy Topp +1

In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties of this new operation,…

cs.DM2015

Hangable Graphs

Mateusz Miotk, Jerzy Topp

Let $G = (V_{G}, E_{G})$ be a connected graph. The distance $d_{G} (u, v)$ between vertices $u$ and $v$ in $G$ is the length of a shortest $u - v$ path in $G$ . The eccentricity of a vertex $v$ …

math.CO2013★ 4 cited

Domination subdivision and domination multisubdivision numbers of graphs

Magda Dettlaff, Joanna Raczek, Jerzy Topp

The \emph{domination subdivision number} sd $(G)$ of a graph $G$ is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to in…

On total domination subdivision numbers of trees

Characterization of α-excellent 2-trees

On α-excellent graphs

Common domination perfect graphs

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

Bipartization of graphs

Graphs with equal domination and covering numbers

On domination perfect graphs

On accurate domination in graphs

Graphs with equal domination and certified domination numbers

Certified domination

Coronas and domination subdivision number of a graph

Hangable Graphs

Domination subdivision and domination multisubdivision numbers of graphs

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

On $α$ -excellent graphs