相关论文: Nonstandard Graphs

This paper proves limit theorems for the number of monochromatic edges in uniform random colorings of general random graphs. These can be seen as generalizations of the birthday problem (what is the chance that there are two friends with…

This report is an improvement of a prior report (Report 813). It sharpens the principal theorems (Theorems 4.2 and 11.2 of Report 813) while simplifying their proofs. There are also several minor changes involving clarifications and…

Let $G(V, E)$ be a simple connected graph, with $|E| = \epsilon.$ In this paper, we define an edge-set graph $\mathcal G_G$ constructed from the graph $G$ such that any vertex $v_{s,i}$ of $\mathcal G_G$ corresponds to the $i$-th…

A graph is \emph{fan-crossing free} if it has a drawing in the plane so that each edge is crossed by independent edges, that is the crossing edges have distinct vertices. On the other hand, it is \emph{fan-crossing} if the crossing edges…

The processes of constructing some graphs from others using binary operations of union with intersection (gluing) are studied. For graph classes closed with respect to gluing operations the elemental and operational bases are introduced.…

A graph is a mathematical object consisting of a set of vertices and a set of edges connecting vertices. Graphs can be drawn on paper in various ways, but until recently all published methods of drawing graphs have had undesirable…

We study the problem of generating graphs with prescribed degree sequences for bipartite, directed, and undirected networks. We first propose a sequential method for bipartite graph generation and establish a necessary and sufficient…

We analyze a minimal model of a growing network. At each time step, a new vertex is added; then, with probability delta, two vertices are chosen uniformly at random and joined by an undirected edge. This process is repeated for t time…

A random intersection graph is constructed by independently assigning a subset of a given set of objects $W,$ to each vertex of the vertex set $V$ of a simple graph $G.$ There is an edge between two vertices of $V,$ iff their respective…

Many systems comprising entities in interactions can be represented as graphs, whose structure gives significant insights about how these systems work. Network theory has undergone further developments, in particular in relation to…

The Spectral Excess Theorem (SPET) for distance-regular graphs states that a regular (connected) graph is distance-regular if and only if its spectral-excess equals its average excess. Recently, some local or global approaches to the SPET…

We construct infinite families of graphs that are determined by their generalized spectrum. This construction is based on new formulae for the determinant of the walk matrix of a graph. The graphs constructed here all satisfy a lower…

A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction number of the graph is the number of such sequences. We determine…

We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…

A non-aligned drawing of a graph is a drawing where no two vertices are in the same row or column. Auber et al. showed that not all planar graphs have non-aligned drawings that are straight-line, planar, and in the minimal-possible $n\times…

A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…

Let $G$ be a simple undirected graph. The regular number of $G$ is defined to be the minimum number of subsets into which the edge set of $G$ can be partitioned so that the subgraph induced by each subset is regular. In this work, we obtain…

In Chapter 8 of the Book, ``Graphs and Networks: Transfinite and Nonstandard'' (published by Birkhauser-Boston in 2004), nonstandard versions of transfinite graphs and of electrical networks having such graphs were defined and examined but…

We give a nonstandard treatment of the notion of ends of proper geodesic metric spaces. We then apply this nonstandard treatment to Cayley graphs of finitely generated groups and give nonstandard proofs of many of the fundamental results…

We propose and investigate a unifying class of sparse random graph models, based on a hidden coloring of edge-vertex incidences, extending an existing approach, Random graphs with a given degree distribution, in a way that admits a…