相关论文: Enumerating planar locally finite Cayley graphs
Harary and Palmer announced an enumeration problem of labelled self-complementary graphs at the end of their book (Graphical Enumeration, Academic Press, New York and London, 1973). This paper resolves this problem. A method for solving…
Deterministic graph grammars generate regular graphs, that form a structural extension of configuration graphs of pushdown systems. In this paper, we study a probabilistic extension of regular graphs obtained by labelling the terminal arcs…
In this study, we investigate the problem of classifying, characterizing, and designing efficient algorithms for hard inference problems on planar graphs, in the limit of infinite size. The problem is considered hard if, for a deterministic…
Probabilistic topic modeling is a popular and powerful family of tools for uncovering thematic structure in large sets of unstructured text documents. While much attention has been directed towards the modeling algorithms and their various…
We consider variants of the clustered planarity problem for level-planar drawings. So far, only convex clusters have been studied in this setting. We introduce two new variants that both insist on a level-planar drawing of the input graph…
We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…
This paper focuses on finite-time in-network computation of linear transforms of distributed graph data. Finite-time transform computation problems are of interest in graph-based computing and signal processing applications in which the…
In this article we study fine regularity properties for mappings of finite distortion. Our main theorems yield strongly localized regularity results in the borderline case in the class of maps of exponentially integrable distortion.…
An intense activity is nowadays devoted to the definition of models capturing the properties of complex networks. Among the most promising approaches, it has been proposed to model these graphs via their clique incidence bipartite graphs.…
The present paper is the first one in the sequence of papers about a simple class of {\em framed $4$-graphs}; the goal of the present paper is to collect some well-known results on planarity and to reformulate them in the language of {\em…
In this paper, we investigate the existence of quantum fractional revival in unitary Cayley graphs over finite commutative rings with identity. We characterize all finite local rings that permit quantum fractional revival in their unitary…
We describe symbolic constructions for listing and enumerating graphs having the same induced edge label sequence. We settle in the affirmative R. Whitty's [W08] conjectured existence of determinantal constructions for listing and…
We state a combinatorial optimization problem whose feasible solutions define both a decomposition and a node labeling of a given graph. This problem offers a common mathematical abstraction of seemingly unrelated computer vision tasks,…
This paper considers the topological degree of $G$-shifts of finite type for the case where $G$ is a nonabelian monoid. Whenever the Cayley graph of $G$ has a finite representation and the relationships among the generators of $G$ are…
We prove that a Cayley graph can be embedded in the euclidean plane without accumulation points of vertices if and only if it is the 1-skeleton of a Cayley complex that can be embedded in the plane after removing redundant simplices. We…
We prove a general multi-dimensional central limit theorem for the expected number of vertices of a given degree in the family of planar maps whose vertex degrees are restricted to an arbitrary (finite or infinite) set of positive integers…
The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…
In this paper, we will study the chromatic number of Cayley graphs of algebraic groups that arise from algebraic constructions. Using Lang-Weil bound and representation theory of finite simple groups of Lie type, we will establish lower…
In this paper, we develop a theory of equipped graded graphs (or Bratteli diagrams) and an alternative theory of projective limits of finite-dimensional simplices. An equipment is an additional structure on the graph, namely, a system of…
Colouring problems arising from group-based constructions provide a natural link between combinatorics and algebra, particularly in the study of Cayley graphs and Latin squares. We introduce the notion of colouring bijections of finite…