S. Cichacz

activity

20082026

most citedDistance magic labeling and two products of graphs

20 citations · 124 across the 27 of their papers we have counts for

collaborators

29 papers

math.CO2026

Note on a magic rectangle set on dihedral group

Sylwia Cichacz

Let $Γ$ be a group of order $mnk$ and $M R S_{Γ} (m, n; k) = (a_{i, j}^{s})_{m \times n}$ be a collection of $k$ arrays $m \times n$ whose entries are all distinct elements of $Γ$ . If there exis…

math.CO2026

Note on zero-sum magic squares on Abelian groups

Sylwia Cichacz, Dalibor Froncek

Let $(Γ, +)$ be an Abelian group of order $n^{2}$ . A $Γ$ -magic square of order $n$ is an $n \times n$ array whose entries are pairwise distinct elements of $Γ$ such that all row sums,…

math.CO2026

Semi-magic dihedral squares

Sylwia Cichacz, Dalibor Froncek

Let $Γ$ be a group of order $n^{2}$ and $S M S_{Γ} (n) = (a_{i, j})_{n \times n}$ be an $n \times n$ array whose entries are all distinct elements of $Γ$ . If there exists an element $μ \in Γ$ su…

math.CO2025

Open XOR-magic odd graphs and closed XOR-magic even graphs

Sylwia Cichacz, Hubert Grochowski, Rita Zuazua

XOR-magic graph labelings form a special subclass of group distance magic labelings. A simple connected graph of order $2^{n}$ is called an open (respectively, closed) XOR-magic grap…

math.CO2025

On rainbow caterpillars in elementary $p$ -groups

Sylwia Cichacz, Barbara Krupińska, Mariusz Woźniak

Given a finite Abelian group $(A, +)$ , consider a tree $T$ with $∣ A ∣$ vertices. The labeling $f : V (T) \to A$ of the vertices of some graph $G$ induces an edge labelin…

math.CO2025★ 1 cited

Group distance magic cubic graphs

Sylwia Cichacz, Štefko Miklavič

A $Γ$ \emph{-distance magic labeling} of a graph $G = (V, E)$ with $∣ V ∣ = n$ is a bijection $ℓ$ from $V$ to an Abelian group $Γ$ of order $n$ , for which there exists $μ \in Γ$ , su…

math.CO2024

Disjoint zero-sum subsets in Abelian groups and its application -- survey

Sylwia Cichacz

We provide a summary of research on disjoint zero-sum subsets in finite Abelian groups, which is a branch of additive group theory and combinatorial number theory. An orthomorphism…

math.CO2024★ 1 cited

Partition of Abelian groups into zero-sum sets by complete mappings and its application to the existence of a magic rectangle set

Sylwia Cichacz

A complete mapping of a group $Γ$ is a bijection $φ : Γ \to Γ$ for which the mapping $x \mapsto x + φ (x)$ is a bijection. In this paper we consider the existence of a complete map…

math.CO2024

Combinatorial spectra using polynomials

Sylwia Cichacz, Martin Dzúrik

In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings.…

math.CO2023

Minimum $k$ -critical-bipartite graphs: the irregular Case

Sylwia Cichacz, Agieszka Görlich, Karol Suchan

We study the problem of finding a minimum $k$ -critical-bipartite graph of order $(n, m)$ : a bipartite graph $G = (U, V; E)$ , with $∣ U ∣ = n$ , $∣ V ∣ = m$ , and $n > m > 1$ , which is $k$ -critical-bi…

math.CO2023★ 1 cited

Group irregularity strength of disconnected graphs

Sylwia Cichacz, Barbara Krupińska

We investigate the \textit{group irregular strength} $(s_{g} (G))$ of graphs, i.e the smallest value of $s$ such that for any Abelian group $Γ$ of order $s$ exists a function $g\colon…

math.CO2023

Irregular labeling on Abelian groups of digraphs

Sylwia Cichacz

Let $G$ be a directed graph of order $n$ with no component of order less than $4$ , and let $Γ$ be a finite Abelian group such that $∣Γ∣ \geq n + 6$ . We show that ther…

math.CO2022★ 4 cited

On b-acyclic chromatic number of a graph

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G$ be a graph. We introduce the acyclic b-chromatic number of $G$ as an analogue to the b-chromatic number of $G$ . An acyclic coloring of a graph $G$ is a map $c:V(G)\rightarr…

math.CO2021★ 3 cited

On some graph-cordial Abelian groups

Sylwia Cichacz

Hovey introduced $A$ -cordial labelings as a generalization of cordial and harmonious labelings \cite{Hovey}. If $A$ is an Abelian group, then a labeling $f \colon V (G) \rightarrow…

math.CO2019★ 8 cited

Group distance magic Cartesian product of two cycles

Sylwia Cichacz, Dalibor Froncek, Paweł Dyrlaga

Let $G = (V, E)$ be a graph and $Γ$ an Abelian group both of order $n$ . A $Γ$ -distance magic labeling of $G$ is a bijection $ℓ : V \to Γ$ for which there exists $μ\in Γ…

math.CO2019★ 4 cited

Realization of digraphs in Abelian groups and its consequences

Sylwia Cichacz, Zsolt Tuza

Let $G$ be a directed graph with no component of orderless than~ $3$ , and let $Γ$ be a finite Abelian group such that $∣Γ∣ \geq 4∣ V (G) ∣$ or if $|V(\…

math.CO2017

Group twin coloring of graphs

Sylwia Cichacz, Jakub Przybyło

For a given graph $G$ , the least integer $k \geq 2$ such that for every Abelian group $G$ of order $k$ there exists a proper edge labeling $f : E (G) \to G$ …

math.CO2017★ 2 cited

Note on group irregularity strength of disconnected graphs

Marcin Anholcer, Sylwia Cichacz, Rafal Jura +1

We investigate the \textit{group irregularity strength} ( $s_{g} (G)$ ) of graphs, i.e. the smallest value of $s$ such that taking any Abelian group $\gr$ of order $s$ , there exists a f…

math.CO2017★ 4 cited

Zero sum partition into sets of the same order and its applications

Sylwia Cichacz

We will say that an Abelian group $Γ$ of order $n$ has the $m$ -\emph{zero-sum-partition property} ( $m$ -\textit{ZSP-property}) if $m$ divides $n$ , $m \geq 2$ and there is a partition…

math.CO2015★ 14 cited

Spectra of Graphs and Closed Distance Magic Labelings

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin

Let $G = (V, E)$ be a graph of order $n$ . A closed distance magic labeling of $G$ is a bijection $ℓ : V (G) \to {1, \dots, n}$ for which there exists a positive intege…

math.CO2013★ 4 cited

Group distance magic and antimagic graphs

S. Cichacz, D. Froncek, K. Sugeng +1

Given a graph $G$ with $n$ vertices and an Abelian group $A$ of order $n$ , an $A$ -distance antimagic labelling of $G$ is a bijection from $V (G)$ to $A$ such that the vertices of $G…

math.CO2013★ 5 cited

Note on group distance magic complete bipartite graphs

Sylwia Cichacz

A $Γ$ -distance magic labeling of a graph $G = (V, E)$ with $∣ V ∣ = n$ is a bijection $ℓ$ from $V$ to an Abelian group $Γ$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}…

math.CO2013★ 12 cited

Group distance magic graphs $G \times C_{n}$

Sylwia Cichacz

A $Γ$ -distance magic labeling of a graph $G = (V, E)$ with $∣ V ∣ = n$ is a bijection $f$ from $V$ to an Abelian group $Γ$ of order $n$ such that the weight $w(x)=\sum_{y\in N_G(x)}f(y…

math.CO2012★ 20 cited

Distance magic labeling and two products of graphs

Marcin Anholcer, Sylwia Cichacz, Iztok Peterin +1

Let $G = (V, E)$ be a graph of order $n$ . A distance magic labeling of $G$ is a bijection $ℓ : V \to 1, ..., n$ for which there exists a positive integer $k$ such that…

Note on a magic rectangle set on dihedral group

Note on zero-sum magic squares on Abelian groups

Semi-magic dihedral squares

Open XOR-magic odd graphs and closed XOR-magic even graphs

On rainbow caterpillars in elementary p-groups

Group distance magic cubic graphs

Disjoint zero-sum subsets in Abelian groups and its application -- survey

Partition of Abelian groups into zero-sum sets by complete mappings and its application to the existence of a magic rectangle set

Combinatorial spectra using polynomials

Minimum k-critical-bipartite graphs: the irregular Case

Group irregularity strength of disconnected graphs

Irregular labeling on Abelian groups of digraphs

On b-acyclic chromatic number of a graph

On some graph-cordial Abelian groups

Group distance magic Cartesian product of two cycles

Realization of digraphs in Abelian groups and its consequences

Group twin coloring of graphs

Note on group irregularity strength of disconnected graphs

Zero sum partition into sets of the same order and its applications

Spectra of Graphs and Closed Distance Magic Labelings

Group distance magic and antimagic graphs

Note on group distance magic complete bipartite graphs

Group distance magic graphs G×Cn​

Distance magic labeling and two products of graphs

On rainbow caterpillars in elementary $p$ -groups

Minimum $k$ -critical-bipartite graphs: the irregular Case

Group distance magic graphs $G \times C_{n}$