Related papers: On a novel graph associated with the circular spac…
We characterize the bipartite graphs that minimize the (first-degree based) entropy, among all bipartite graphs of given size, or given size and (upper bound on the) order. The extremal graphs turn out to be complete bipartite graphs, or…
For any metric $d$ on $\mathbb{R}^2$, an ($\mathbb{R}^2,d$)-geometric graph is a graph whose vertices are points in $\mathbb{R}^2$, and two vertices are adjacent if and only if their distance is at most 1. If $d=\|.\|_{\infty}$, the metric…
Let $G=(V,E)$ be a graph. A set of vertices $A$ is an incidence generator for $G$ if for any two distinct edges $e,f\in E(G)$ there exists a vertex from $A$ which is an endpoint of either $e$ or $f$. The smallest cardinality of an incidence…
We study the basic properties of a prime sum graph, which is a simple graph defined on $\mathbb N$ where two vertices are adjacent if and only if their sum is a prime number. Further, we investigate some specific structures that appear…
For each positive integer $n$, we define the divisibility relation graph $D_n$ whose vertex set is the set of divisors of $n$, and in which two vertices are adjacent if one is a divisor of the other. This type of graph is a special case of…
In this paper, we propose a new type of graph, denoted as "embedded-graph", and its theory, which employs a distributed representation to describe the relations on the graph edges. Embedded-graphs can express linguistic and complicated…
We present the theory of multifunctions applied to graphs. Its interesting feature is that walks are recognized as iterations. We consider the graphs with arbitrary number of vertices which are determined by multifunctions. The mutually…
In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using…
We present a direct and fairly simple proof of the following incidence bound: Let $P$ be a set of $m$ points and $L$ a set of $n$ lines in ${\mathbb R}^d$, for $d\ge 3$, which lie in a common algebraic two-dimensional surface of degree $D$…
In this paper, we extend the recently introduced concept of partially dual ribbon graphs to graphs. We then go on to characterize partial duality of graphs in terms of bijections between edge sets of corresponding graphs. This result…
A geometric graph is a graph drawn in the plane so that its vertices and edges are represented by points in general position and straight line segments, respectively. A vertex of a geometric graph is called pointed if it lies outside of the…
The paper starts with discussion of applications of cycle spaces to transportation cost. After a short survey of the known results on cycle spaces, we turn to the study of minimal projections onto cycle spaces in the corresponding…
A speculative overview of a future topic of research. The paper is a collection of ideas concerning two related areas: 1) Graph computation machines ("computing with graphs"). This is the class of models of computation in which the state of…
Random intersection graphs are characterized by three parameters: $n$, $m$ and $p$, where $n$ is the number of vertices, $m$ is the number of objects, and $p$ is the probability that a given object is associated with a given vertex. Two…
Binomial Cayley graphs are obtained by considering the binomial coefficient of the weight function of a given Cayley graph and a natural number. We introduce these objects and study two families: one associated with symmetric groups and the…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…
We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…
The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an…
We characterise rigid graphs for cylindrical normed spaces $Z=X\oplus_\infty \mathbb{R}$ where $X$ is a finite dimensional real normed linear space and $Z$ is endowed with the product norm. In particular, we obtain purely combinatorial…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…