相关论文: On finite edge-primitive and edge-quasiprimitive g…

Let $G$ be a permutation group on a set $\Omega$. A subset of $\Omega$ is a base for $G$ if its pointwise stabiliser in $G$ is trivial. In this paper we introduce and study an associated graph $\Sigma(G)$, which we call the Saxl graph of…

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. For all $s \geq 1$, we obtain upper bounds for reg$(I(G)^s)$ for bipartite graphs. We then compare the properties of $G$ and $G'$, where $G'$ is the graph…

In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the…

The prime-coprime graph $\Theta(G)$ of a finite group $G$ is the simple graph with vertex set $G$, where two distinct elements are adjacent whenever the greatest common divisor of their orders is either $1$ or a prime. We characterize all…

A group $G$ of permutations of a set $\Omega$ is {\em primitive} if it acts transitively on $\Omega$, and the only $G$-invariant equivalence relations on $\Omega$ are the trivial and universal relations. A graph $\Gamma$ is {\em primitive}…

Some classical graph problems such as finding minimal spanning tree, shortest path or maximal flow can be done efficiently. We describe slight variations of such problems which are shown to be NP-complete. Our proofs use straightforward…

The $k$-coprime graph of order $n$ is the graph with vertex set $\{k, k+1, \ldots, k+n-1\}$ in which two vertices are adjacent if and only if they are coprime. We characterize Hamiltonian $k$-coprime graphs. As a particular case, two…

We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or…

Let \pi(G) denote the set of prime divisors of the order of a finite group G. The prime graph of G is the graph with vertex set \pi(G) with edges {p,q} if and only if there exists an element of order pq in G. In this paper, we prove that a…

In this paper, we study the concept of edge-group choosability of graphs. We say that G is edge k-group choosable if its line graph is k-group choosable. An edge-group choosability version of Vizing conjecture is given. The evidence of our…

Let $\mathcal{H}$ be the class of bounded measurable symmetric functions on $[0,1]^2$. For a function $h \in \mathcal{H}$ and a graph $G$ with vertex set $\{v_1,\ldots,v_n\}$ and edge set $E(G)$, define \[ t_G(h) \; = \; \int \cdots \int…

A simple topological graph $G$ is a graph drawn in the plane so that any pair of edges have at most one point in common, which is either an endpoint or a proper crossing. $G$ is called saturated if no further edge can be added without…

A class of graphs is bridge-addable if given a graph $G$ in the class, any graph obtained by adding an edge between two connected components of $G$ is also in the class. The authors recently proved a conjecture of McDiarmid, Steger, and…

We study geometric and topological properties of infinite graphs that are quasi-isometric to a planar graph of bounded degree. We prove that every locally finite quasi-transitive graph excluding a minor is quasi-isometric to a planar graph…

We prove that if an $n$-vertex graph $G$ can be drawn in the plane such that each pair of crossing edges is independent and there is a crossing-free edge that connects their endpoints, then $G$ has $O(n)$ edges. Graphs that admit such…

In this paper, we study 2-geodesic-transitive graphs of order twice an odd prime power. Classifications of corresponding basic graphs and such graphs with almost simple automorphism groups are given, and a reduction theorem for general case…

We give certain properties which are satisfied by the descendant set of a vertex in an infinite, primitive, distance transitive digraph of finite out-valency and provide a strong structure theory for digraphs satisfying these properties. In…

We classify all infinite primitive permutation groups possessing a finite point stabilizer, thus extending the seminal Aschbacher-O'Nan-Scott Theorem to all primitive permutation groups with finite point stabilizers.

Let $G$ be a simple graph. Consider all weightings of the vertices of $G$ with real numbers whose total sum is nonnegative. How many edges of $G$ have endpoints with a nonnegative sum? We consider the minimum number of such edges over all…

A graph is called primitive if its automorphism group acts primitively on the vertex set. In this paper, we prove a classification of the possible distance sequences of locally infinite primitive graphs. In particular we show that if a…