Related papers: Modular flip-graphs of one holed surfaces

The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a…

We consider domino tilings of three-dimensional cubiculated manifolds with or without boundary, including subsets of Euclidean space and three-dimensional tori. In particular, we are interested in the connected components of the space of…

Let $P$ be a set of $n$ points and $Q$ a convex $k$-gon in ${\mathbb R}^2$. We analyze in detail the topological (or discrete) changes in the structure of the Voronoi diagram and the Delaunay triangulation of $P$, under the convex distance…

We present an effective method for recovering the topology of a bordered oriented surface with marked points from its cluster algebra. The information is extracted from the maximal triangulations of the surface, those that have exchange…

The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the…

The structure of a graphene monolayer on Ir(111) has been investigated {\it in situ} in the growth chamber by surface x-ray diffraction including the specular rod, which allows disentangling the effect of the sample roughness from that of…

In this paper we study random graphs with independent and identically distributed degrees of which the tail of the distribution function is regularly varying with exponent $\tau\in (2,3)$. The number of edges between two arbitrary nodes,…

We consider relations between the size, treewidth, and local crossing number (maximum number of crossings per edge) of graphs embedded on topological surfaces. We show that an $n$-vertex graph embedded on a surface of genus $g$ with at most…

We survey basic properties and bounds for $q$-equivelar and $d$-covered triangulations of closed surfaces. Included in the survey is a list of the known sources for $q$-equivelar and $d$-covered triangulations. We identify all orientable…

Let $G$ be a finite, connected graph and $v$ a vertex of $G$. The average distance and the eccentricity of $v$ in $G$ are defined as the arithmetic mean and the maximum, respectively, of the distances from $v$ to all other vertices of $G$.…

Delaunay flip is an elegant, simple tool to convert a triangulation of a point set to its Delaunay triangulation. The technique has been researched extensively for full dimensional triangulations of point sets. However, an important case of…

Let $M_n$ be a simple triangulation of the sphere $S^2$, drawn uniformly at random from all such triangulations with n vertices. Endow $M_n$ with the uniform probability measure on its vertices. After rescaling graph distance on $V(M_n)$ by…

We derive attainable upper bounds on the algebraic connectivity (spectral gap) of a regular graph in terms of its diameter and girth. This bound agrees with the well-known Alon-Boppana-Friedman bound for graphs of even diameter, but is an…

A graph drawn in a surface is a near-quadrangulation if the sum of the lengths of the faces different from 4-faces is bounded by a fixed constant. We leverage duality between colorings and flows to design an efficient algorithm for…

We discuss scaling limits of large bipartite quadrangulations of positive genus. For a given $g$, we consider, for every $n \ge 1$, a random quadrangulation $\q_n$ uniformly distributed over the set of all rooted bipartite quadrangulations…

We study the configuration space of rectangulations and convex subdivisions of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$ elementary flip and rotate operations can transform any rectangulation to any other…

In this paper, we introduce and study a new distance parameter {\it triameter} of a connected graph $G$, which is defined as $max\{d(u,v)+d(v,w)+d(u,w): u,v,w \in V\}$ and is denoted by $tr(G)$. We find various upper and lower bounds on…

We construct a family of finite special 2-groups which have commuting graph of increasing diameter

If a finite group of orientation-preserving diffeomorphisms of the 3-dimensional torus leaves invariant an oriented, closed, embedded surface of genus g>1 and preserves the orientation of the surface, then its order is bounded from above by…

We present a procedure to sample uniformly from the set of combinatorial isomorphism types of balanced triangulations of surfaces - also known as graph-encoded surfaces. For a given number $n$, the sample is a weighted set of graph-encoded…