Related papers: The Structure of the 2-factor Transfer Digraph Com…

Let $G$ be a finite group and $m$ be an integer. We employ the notation $g_i$ to represent elements $(g,i)$ in the Cartesian product $G \times \mathbb{Z}_m$, where $\mathbb{Z}_m$ denotes integers modulo $m$. For given sets $T_{i,j}…

A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. In this paper we present a complete classification of all…

Let $G$ be a finite group. The bipartite divisor graph for the set of irreducible complex character degrees is the undirected graph with vertex set consisting of the prime numbers dividing some character degree and of the non-identity…

A graph $G$ is a prime distance graph (respectively, a 2-odd graph) if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the difference of their labels is prime (either 2 or odd). We prove that…

A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing…

We present an order-theoretic approach to the study of countably infinite locally 2-arc-transitive bipartite graphs. Our approach is motivated by techniques developed by Warren and others during the study of cycle-free partial orders. We…

The 2-switch-degree of $G$ is the number of distinct 2-switches acting on a graph $G$. In this work we study structural properties of the 2-switch-degree, with a focus on split graphs. Our approach is motivated by the Tyshkevich…

We classify trivalent vertex-transitive graphs whose edge sets have a partition into a 2-factor composed of two cycles and a 1-factor that is invariant under the action of the automorphism group.

Let $G$ be a $q$-regular bipartite graph with bipartition $(U,V)$. It was proved by Lu, Wang, and Yan in 2020 that $G$ has a spanning subgraph $H$ such that each vertex of $U$ has degree 1 in $H$, and each vertex of $V$ has degree distinct…

We prove that a strongly connected balanced bipartite directed graph of order $2a\geq 6$ with partite sets $X$ and $Y$ contains cycles of every length $2, 4, \ldots , 2a$, provided $d(x)+d(y)\geq 3a$ for every pair of vertices $x$, $y$…

A bipartite graph is {\em pseudo 2--factor isomorphic} if all its 2--factors have the same parity of number of circuits. In \cite{ADJLS} we proved that the only essentially 4--edge-connected pseudo 2--factor isomorphic cubic bipartite graph…

It is shown that each subgroup of odd index in an alternating group of degree at least 10 has all insoluble composition factors to be alternating. A classification is then given of 2-arc-transitive graphs of odd order admitting an…

Mixed graphs can be seen as digraphs with arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite and in which the undirected and directed degrees are one. The best graphs,…

In multivariate statistics, acyclic mixed graphs with directed and bidirected edges are widely used for compact representation of dependence structures that can arise in the presence of hidden (i.e., latent or unobserved) variables. Indeed,…

A graph is pseudo 2-factor isomorphic if all of its 2-factors have the same parity of number of cycles. Abreu et al. [J. Comb. Theory, Ser. B. 98 (2008) 432--442] conjectured that $K_{3,3}$, the Heawood graph and the Pappus graph are the…

We study the typical structure and the number of triangle-free graphs with $n$ vertices and $m$ edges where $m$ is large enough so that a typical triangle-free graph has a cut containing nearly all of its edges, but may not be bipartite.…

R. Wang (Discrete Mathematics and Theoretical Computer Science, vol. 19(3), 2017) proposed the following problem. \textbf{Problem.} Let $D$ be a strongly connected balanced bipartite directed graph of order $2a\geq 8$. Suppose that…

A graph $X$ is 2-spanning cyclable if for any pair of distinct vertices $u$ and $v$ there is a 2-factor of $X$ consisting of two cycles such that $u$ and $v$ belong to distinct cycles. In this paper we examine the 2-spanning cyclability of…

A pseudo [2,b]-factor of a graph G is a spanning subgraph in which each component C on at least three vertices is a [2,b]-graph. The main contibution of this paper, is to give an upper bound to the number of components that are edges or…

A digraph is 2-regular if every vertex has both indegree and outdegree two. We define an embedding of a 2-regular digraph to be a 2-cell embedding of the underlying graph in a closed surface with the added property that for every…