相关论文: Regular maps of order $2$-powers

In this paper the problem of the existence of regular nut graphs is addressed. A generalization of Fowler's Construction which is a local enlargement applied to a vertex in a graph is introduced to generate nut graphs of higher order. Let…

For all positive even integers $n$, graphs of order $n$ with degree sequence \begin{equation*} S_{n}:1,2,\dots,n/2,n/2,n/2+1,n/2+2,\dots,n-1 \end{equation*} naturally arose in the study of a labeling problem in \cite{IMO}. This fact…

The normal form for an n-dimensional map with irreducible nilpotent linear part is determined using sl2-representation theory. We sketch by example how the reducible case can also be treated in an algorithmic manner. The construction (and…

A nut graph is a simple graph whose adjacency matrix is singular with $1$-dimensional kernel such that the corresponding eigenvector has no zero entries. In 2020, Fowler et al. characterised for each $d \in \{3,4,\ldots,11\}$ all values $n$…

In this work we compare the semialgebraic subsets that are images of regulous maps with those that are images of regular maps. Recall that a map f : R n $\rightarrow$ R m is regulous if it is a rational map that admits a continuous…

The vertices of a graph are classified into seven types by J.T. Hedetniemi, S.M. Hedetniemi, S.T. Hedetniemi and T.M. Lewis and they ask the following questions: 1) What is the smallest order $n$ of a graph having $n-2$ very typical…

A graph $\Gamma$ is basic if Aut$\Gamma$ has no normal subgroup $N\ne1$ such that $\Gamma$ is a normal cover of the normal quotient graph $\Gamma_N$. In this paper, we completely determine the basic normal quotient graphs of all connected…

For each integer \( n \geq 3 \), we construct a self-dual regular 3-polytope \( \mathcal{P} \) of type \( \{n, n\} \) with \( 2^n n \) flags, resolving two foundamental open questions on the existence of regular polytopes with certain…

Previous research established that the maximal rank of the abstract regular polytopes whose automorphism group is a transitive proper subgroup of $\mbox{S}_n$ is $n/2 + 1$. Up to isomorphism and duality, when $n\geq 12$, there are only two…

Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…

The paper characterizes $(2t+1)$-regular graphs with circular flow number $2 + \frac{2}{2t-1}$. For $t=1$ this is Tutte's characterization of cubic graphs with flow number 4. The class of cubic graphs is the only class of odd regular graphs…

We search for rational, four-dimensional maps of standard type (x_{n+1} - 2x_n + x_{n-1} = eps f(x,eps)) possessing one or two polynomial integrals. There are no non-trivial maps corresponding to cubic oscillators, but we find a…

In this paper, we focus on the class of complete $S$-partite graphs, for $S$ an undirected graph possibly with self-loops, and address the problem of finding largest $2$-regular subgraphs of these graphs, which can be formulated as an…

In this paper, we study prime order automorphisms of generalized quadrangles. We show that, if $\mathcal{Q}$ is a thick generalized quadrangle of order $(s,t)$, where $s > t$ and $s+1$ is prime, and $\mathcal{Q}$ has an automorphism of…

A continous map $f: \mathbb{C}^n \rightarrow \mathbb{C}^N$ is $k$-regular if the image of any $k$ points spans a $k$-dimensional subspace. It is an important problem in topology and interpolation theory, going back to Borsuk and Chebyshev,…

This study is the $2^{nd}$ part of a detailed study on Type-2 isomorphic circulant graphs having ten parts \cite{v2-1}-\cite{v2-10}. Definition of Type-2 isomorphism of circulant graphs $C_n(R)$ w.r.t. $m$ was further modified by the author…

An old problem of Erd\H{o}s, Fajtlowicz and Staton asks for the order of a largest induced regular subgraph that can be found in every graph on n vertices. Motivated by this problem, we consider the order of such a subgraph in a typical…

Two locally generic maps f,g : M^n --> R^{2n-1} are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if n is not 3 and M^n is a closed n-manifold then the regular…

The paper proves two theorems concerning the set of periods of periodic orbits for maps of graphs that are homotopic to the constant map and such that the vertices form a periodic orbit. The first result is that if $v$ is not a divisor of…

In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)-automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and…