Related papers: Geometric graphs on convex point sets
We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$…
For a graph $G$ of order $n$ and with eigenvalues $\lambda_1\geqslant\cdots\geqslant\lambda_n$, the HL-index $R(G)$ is defined as $R(G) ={\max}\left\{|\lambda_{\lfloor(n+1)/2\rfloor}|, |\lambda_{\lceil(n+1)/2\rceil}|\right\}.$ We show that…
A \emph{directional labeling} of an edge $\emph{uv}$ in a graph $G=(V,E)$ by an ordered pair $ab$ is a labeling of the edge $uv$ such that the label on $uv$ in the direction from $u$ to $v$ is $\ell(uv)=ab$, and $\ell(vu)=ba$. New…
A theory of orientation on gain graphs (voltage graphs) is developed to generalize the notion of orientation on graphs and signed graphs. Using this orientation scheme, the line graph of a gain graph is studied. For a particular family of…
Genevois introduced and investigated mediangle graphs as a common generalization of median graphs (1-sekeleta of CAT(0) cube complexes) and Coxeter graphs (Cayley graphs of Coxeter systems) and studied groups acting on them. He asked if…
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…
It has been known since 1991 that the problem of recognizing grid intersection graphs is NP-complete. Here we use a modified argument of the above result to show that even if we restrict to the class of unit grid intersection graphs…
Graphs derived from groups are a widely studied class of graphs, motivated by their highly symmetric structure. In particular, G-graphs offer an easy and interesting alternative construction of semi-symmetric graphs. After recalling the…
Let $G$ be a bipartite graph on $n$ vertices with the Laplacian matrix $L_G$. When $G$ is a tree, inequalities involving coefficients of immanantal polynomials of $L_G$ are known as we go up $GTS_n$ poset of unlabelled trees with $n$…
We consider the problem of finding all allowed edges in a bipartite graph $G=(V,E)$, i.e., all edges that are included in some maximum matching. We show that given any maximum matching in the graph, it is possible to perform this…
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…
Recently, graph neural networks have been adopted in a wide variety of applications ranging from relational representations to modeling irregular data domains such as point clouds and social graphs. However, the space of graph neural…
The disjoint convex obstacle number of a graph G is the smallest number h such that there is a set of h pairwise disjoint convex polygons (obstacles) and a set of n points in the plane (corresponding to V(G)) so that a vertex pair uv is an…
A complex unit gain graph is a simple graph in which each orientation of an edge is given a complex number with modulus 1 and its inverse is assigned to the opposite orientation of the edge. In this article, first we establish bounds for…
Graph convexity spaces have been studied in many contexts. In particular, some studies are devoted to determine if a graph equipped with a convexity space is a {\em convex geometry}. It is well known that chordal and Ptolemaic graphs can be…
Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of the similar type, called linearized Wenger graphs. The spectrum, diameter and girth of these linearized Wenger graphs are…
Bipartite graph embedding has recently attracted much attention due to the fact that bipartite graphs are widely used in various application domains. Most previous methods, which adopt random walk-based or reconstruction-based objectives,…
We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges…
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…
This paper is the first from a series of papers that provide a characterization of maximum packings of $T$-cuts in bipartite graphs. Given a connected graph, a set $T$ of an even number of vertices, and a minimum $T$-join, an edge weighting…