Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.

IGraph/M is an efficient general purpose graph theory and network analysis package for Mathematica. serves as the Wolfram Language interfaces to igraph C library, also provides several unique pieces of functionality not yet present in igraph, but made possible by combining its capabilities with Mathematica's. The designed support both theoretical research well large-scale empirical networks.

A Vietoris–Rips complex R is the clique complex of a proximity graph. This graph can arise from a finite set of points in Euclidean n-space, and then there is a natural projection onto its n-dimensional shadow; p : R æ S. An article by Chambers et al.[Cha+10] demonstrates that p induces an isomorphism of fundamental groups for n = 1, 2, while the induced homomorphism fails to be surjective for ...

In this article we analyze the response of Time of Flight cameras (active sensors) for close range imaging under three different illumination conditions and compare the results with stereo vision (passive) sensors. Time of Flight sensors are sensitive to ambient light and have low resolution but deliver high frame rate accurate depth data under suitable conditions. We introduce some metrics for...

In this study, we propose an automatic detection algorithm for cloud/shadow on remote sensing optical images. It is based on physical properties of clouds and shadows, namely for a cloud and its associated shadow: both are connex objects of similar shape and area, and they are related by their relative locations. We show that these properties can be formalized using Markov Random Field (MRF) fr...

Let $G$ be a simple graph of order $n$ and size $m$.The edge covering of $G$ is a set of edges such that every vertex of $G$ is incident to at least one edge of the set. The edge cover polynomial of $G$ is the polynomial$E(G,x)=sum_{i=rho(G)}^{m} e(G,i) x^{i}$,where $e(G,i)$ is the number of edge coverings of $G$ of size $i$, and$rho(G)$ is the edge covering number of $G$. In this paper we stud...