Related papers: Fission of Halving Edges Graphs
Theta graphs are important geometric graphs that have many applications, including wireless networking, motion planning, real-time animation, and minimum-spanning tree construction. We give closed form expressions for the average degree of…
In this work, we study the computability of topological graphs, which are obtained by gluing arcs and rays together at their endpoints. We prove that every semicomputable graph in a computable metric space can be approximated, with…
A numerical semigroup $S$ is an additively-closed set of non-negative integers, and a factorization of an element $n$ of $S$ is an expression of $n$ as a sum of generators of $S$. It is known that for a given numerical semigroup $S$, the…
We exhibit a characteristic structure of the class of all regular graphs of degree d that stems from the spectra of their adjacency matrices. The structure has a fractal threadlike appearance. Points with coordinates given by the mean and…
We study the problem of edge partitioning, where the goal is to partition the edge set of a graph into several parts. The replication factor of a vertex $v$ is the number of parts that contain edges incident to $v$. The goal is to minimize…
In a previous paper, we showed how certain orientations of the edges of a graph G embedded in a closed oriented surface S can be understood as discrete spin structures on S. We then used this correspondence to give a geometric proof of the…
Suppose a finite, unweighted, combinatorial graph $G = (V,E)$ is the union of several (degree-)regular graphs which are then additionally connected with a few additional edges. $G$ will then have only a small number of vertices $v \in V$…
When applying automatic analysis of fluorescence or histopathological images of cells, it is necessary to partition, or de-clump, partially overlapping cell nuclei. In this work, I describe a method of partitioning partially overlapping…
The intersection graph induced by a set $\Disks$ of $n$ disks can be dense. It is thus natural to try and sparsify it, while preserving connectivity. Unfortunately, sparse graphs can always be made disconnected by removing a small number of…
Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k are removed until there are no vertices of degree less than k left. The remaining hypergraph…
An arithmetical structure on a graph is given by a labeling of the vertices which satisfies certain divisibility properties. In this note, we look at several families of graphs and attempt to give counts on the number of arithmetical…
The line graph of a graph $G$ is the graph $L(G)$ whose vertex set is the edge set of $G$ and there is an edge between $e,f\in E(G)$ if $e$ and $f$ share an endpoint in $G$. A graph is called line graph if it is a line graph of some graph.…
Fuzzy incidence graphs (FIG) model real world problems efficiently when there is an extra attribute of vertex-edge relationship. The article discusses the operations on Fuzzy incidence graphs. The join, Cartesian product, tensor product,…
The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of…
For a given group $G$ the orientably regular maps with orientation-preserving automorphism group $G$ are used as the vertices of a graph $\O(G)$, with undirected and directed edges showing the effect of duality and hole operations on these…
The splitting-off operation in undirected graphs is a fundamental reduction operation that detaches all edges incident to a given vertex and adds new edges between the neighbors of that vertex while preserving their degrees. Lov\'asz (1974)…
We describe the construction of the slice fibration of a given one.
The graph bisection problem is the problem of partitioning the vertex set of a graph into two sets of given sizes such that the sum of weights of edges joining these two sets is optimized. We present a semidefinite programming relaxation…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…