D. Froncek

activity

20082025

most citedGroup distance magic Cartesian product of two cycles

8 citations · 16 across the 9 of their papers we have counts for

collaborators

9 papers

math.CO2025

Magic squares on Abelian groups

Sylwia Cichacz, Dalibor Froncek

Let $(Γ, +)$ be an Abelian group of order $n^{2}$ and MS $_{Γ} (n)$ be an $n \times n$ array whose entries are all elements of $Γ$ . Then MS $_{Γ} (n)$ is a $Γ$ -magic square if all row, column,…

math.CO2024

On some classes of cycles-related $Γ$ -harmonious graphs

Gyaneshwar Agrahari, Dalibor Froncek

A graph $G (V, E)$ is $Γ$ -harmonious when there is an injection $f$ from $V$ to an Abelian group $Γ$ such that the induced edge labels defined as $w (x y) = f (x) + f (y)$ form a bijection f…

math.CO2022

Supermagic labeling of $C_{n} □ C_{m}$

Dalibor Froncek

A supermagic labeling (often also called supermagic labeling) of a graph $G (V, E)$ with $∣ E ∣ = k$ is a bijection from $E$ to the set of first $k$ positive integers such that the sum o…

math.CO2019★ 1 cited

2-nearly Platonic graphs are unique

D. Froncek, M. R. Khorsandi, S. R. Musawi +1

A 2-nearly Platonic graph of type (k|d) is a k-regular planar graph with f faces, f-2 of which are of degree d and the remaining two are of degrees m_1;m_2, both different from d.…

math.CO2019

A note on nearly Platonic graphs with connectivity one

D. Froncek, M. R. Khorsandi, S. R. Musawi +1

A k-regular planar graph G is nearly Platonic when all faces but one are of the same degree while the remaining face is of a different degree. We show that no such graphs with conn…

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.CO2016★ 2 cited

A note on nearly platonic graphs

Dalibor Froncek, William J. Keith, Donald L. Kreher

A nearly platonic graph is a k-regular simple planar graph in which all but a small number of the faces have the same degree. We show that it is impossible for a finite graph to ha…

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.CO2008★ 1 cited

Super edge-graceful paths

Sylwia Cichacz, Dalibor Froncek, Wenjie Xu

A graph $G (V, E)$ of order $∣ V ∣ = p$ and size $∣ E ∣ = q$ is called super edge-graceful if there is a bijection $f$ from $E$ to ${0, \pm 1, \pm 2, ..., \pm \frac{q - 1}{2}}$ when $q$ is odd a…