Related papers: Graphs Embedded into Finite Projective Planes

Feature extraction and dimension reduction for networks is critical in a wide variety of domains. Efficiently and accurately learning features for multiple graphs has important applications in statistical inference on graphs. We propose a…

There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…

The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…

We introduce a novel embedding method diverging from conventional approaches by operating within function spaces of finite dimension rather than finite vector space, thus departing significantly from standard knowledge graph embedding…

We report on recent progress concerning the relationship that exists between the algebraic structure of a finite group and certain features of its class-size prime graph.

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 construct a class of bounded degree bipartite graphs with a small separator and large bandwidth. Furthermore, we also prove that graphs from this class are spanning subgraphs of graphs with minimum degree just slightly…

We study the simultaneous embeddability of a pair of partitions of the same underlying set into disjoint blocks. Each element of the set is mapped to a point in the plane and each block of either of the two partitions is mapped to a region…

A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on…

Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…

The symmetries of complex molecular structures can be modeled by the {\em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular…

Network embedding assigns nodes in a network to low-dimensional representations and effectively preserves the network structure. Recently, a significant amount of progresses have been made toward this emerging network analysis paradigm. In…

Topological drawings are natural representations of graphs in the plane, where vertices are represented by points, and edges by curves connecting the points. Topological drawings of complete graphs and of complete bipartite graphs have been…

Let $\Gamma$ be a finite graph and let $\Gamma^{\mathrm{e}}$ be its extension graph. We inductively define a sequence $\{\Gamma_i\}$ of finite induced subgraphs of $\Gamma^{\mathrm{e}}$ through successive applications of an operation called…

We prove that there is an algorithm to determine if a given finite graph is an induced subgraph of a given curve graph.

We find a family of planar bipartite graphs all of whose Lombardi drawings (drawings with circular arcs for edges, meeting at equal angles at the vertices) are nonplanar. We also find families of embedded series-parallel graphs and…

This note is on the structures of line graphs and 2-variegated graphs. We have given here solutions of some graph equations involving line graphs and 2-variegated graphs.

The recent proliferation of publicly available graph-structured data has sparked an interest in machine learning algorithms for graph data. Since most traditional machine learning algorithms assume data to be tabular, embedding algorithms…

Graph transformations definable in logic can be described using the notion of transductions. By understanding transductions as a basic embedding mechanism, which captures the possibility of encoding one graph in another graph by means of…

Graph analytics can lead to better quantitative understanding and control of complex networks, but traditional methods suffer from high computational cost and excessive memory requirements associated with the high-dimensionality and…