Note on cyclic decompositions of complete bipartite graphs into cubes

Dalibor Fronček

Displaying similar documents to “Note on cyclic decompositions of complete bipartite graphs into cubes”

A note on another construction of graphs with $4 n + 6$ vertices and cyclic automorphism group of order $4 n$

Peteris Daugulis (2017)

Archivum Mathematicum

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The problem of finding minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic groups. This problem was considered earlier by other authors. We give a construction of an undirected graph having $4 n + 6$ vertices and automorphism group cyclic of order $4 n$ , $n \geq 1$ . As a special case we get graphs with $2^{k} + 6$ vertices and cyclic automorphism groups of order $2^{k}$ . It can revive interest in related problems.

Kannan-type cyclic contraction results in $2$ -Menger space

Binayak S. Choudhury, Samir Kumar BHANDARI (2016)

Mathematica Bohemica

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In this paper we establish Kannan-type cyclic contraction results in probabilistic 2-metric spaces. We use two different types of $t$ -norm in our theorems. In our first theorem we use a Hadzic-type $t$ -norm. We use the minimum $t$ -norm in our second theorem. We prove our second theorem by different arguments than the first theorem. A control function is used in our second theorem. These results generalize some existing results in probabilistic 2-metric spaces. Our results are illustrated with...

Cyclic Type Fixed Point Results in 2-Menger Spaces

Binayak S. Choudhury, Samir Kumar BHANDARI, Parbati SAHA (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we introduce generalized cyclic contractions through $r$ number of subsets of a probabilistic 2-metric space and establish two fixed point results for such contractions. In our first theorem we use the Hadzic type $t$ -norm. In another theorem we use a control function with minimum $t$ -norm. Our results generalizes some existing fixed point theorem in 2-Menger spaces. The results are supported with some examples.

On the Rockafellar theorem for $Φ^{γ (\cdot, \cdot)}$ -monotone multifunctions

S. Rolewicz (2006)

Studia Mathematica

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Let X be an arbitrary set, and γ: X × X → ℝ any function. Let Φ be a family of real-valued functions defined on X. Let $Γ : X \to 2^{Φ}$ be a cyclic $Φ^{γ (\cdot, \cdot)}$ -monotone multifunction with non-empty values. It is shown that the following generalization of the Rockafellar theorem holds. There is a function f: X → ℝ such that Γ is contained in the $Φ^{γ (\cdot, \cdot)}$ -subdifferential of f, $Γ (x) \subset \partial_{Φ}^{γ (\cdot, \cdot)} {f |}_{x}$ .

On the behaviour of the solutions of a $k$ -order cyclic-type system of max difference equations

Gesthimani Stefanidou, Garyfalos Papaschinopoulos (2025)

Czechoslovak Mathematical Journal

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We investigate the behaviour of the solutions of a $k$ -dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium....

Resolving sets of directed Cayley graphs for the direct product of cyclic groups

Demelash Ashagrie Mengesha, Tomáš Vetrík (2019)

Czechoslovak Mathematical Journal

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A directed Cayley graph $C (Γ, X)$ is specified by a group $Γ$ and an identity-free generating set $X$ for this group. Vertices of $C (Γ, X)$ are elements of $Γ$ and there is a directed edge from the vertex $u$ to the vertex $v$ in $C (Γ, X)$ if and only if there is a generator $x \in X$ such that $u x = v$ . We study graphs $C (Γ, X)$ for the direct product $Z_{m} \times Z_{n}$ of two cyclic groups $Z_{m}$ and $Z_{n}$ , and the generating set $X = {(0, 1), (1, 0), (2, 0), \dots, (p, 0)}$ . We present resolving sets which yield upper bounds on the metric dimension of these graphs for $p = 2$ and $3$ .

Moufang loops of order coprime to three that cyclically extend groups of dihedral type

Aleš Drápal (2016)

Commentationes Mathematicae Universitatis Carolinae

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This paper completely solves the isomorphism problem for Moufang loops $Q = G C$ where $G ⊴ Q$ is a noncommutative group with cyclic subgroup of index two and $| Z (G) | \leq 2$ , $C$ is cyclic, $G \cap C = 1$ , and $Q$ is finite of order coprime to three.

Ramification in quartic cyclic number fields $K$ generated by $x^{4} + p x^{2} + p$

Julio Pérez-Hernández, Mario Pineda-Ruelas (2021)

Mathematica Bohemica

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If $K$ is the splitting field of the polynomial $f (x) = x^{4} + p x^{2} + p$ and $p$ is a rational prime of the form $4 + n^{2}$ , we give appropriate generators of $K$ to obtain the explicit factorization of the ideal $q 𝒪_{K}$ , where $q$ is a positive rational prime. For this, we calculate the index of these generators and integral basis of certain prime ideals.

Remarks on $D$ -integral complete multipartite graphs

Pavel Híc, Milan Pokorný (2016)

Czechoslovak Mathematical Journal

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A graph is called distance integral (or $D$ -integral) if all eigenvalues of its distance matrix are integers. In their study of $D$ -integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on $D$ -integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs $K_{p_{1}, p_{2}, p_{3}}$ with $p_{1} < p_{2} < p_{3}$ , and $K_{p_{1}, p_{2}, p_{3}, p_{4}}$ with $p_{1} < p_{2} < p_{3} < p_{4}$ , as well as the infinite classes of distance integral...