A graph G = (V,E) is said to be 6-mixed-connected if G−U−D is connected for all sets U ⊆ V and D ⊆ E which satisfy 2|U | + |D| ≤ 5. In this note we prove that 6-mixed-connected graphs are (redundantly globally) rigid in the plane. This improves on a previous result of Lovász and Yemini.

Graphical Markov models use graphs, either undirected, directed, or mixed, to represent possible dependences among statistical variables. Applications of undirected graphs (UGs) include models for spatial dependence and image analysis, while acyclic directed graphs (ADGs), which are especially convenient for statistical analysis, arise in such fields as genetics and psychometrics and as models ...

Graphical causal models are an important tool for knowledge discovery because they can represent both the causal relations between variables and the multivariate probability distributions over the data. Once learned, causal graphs can be used for classification, feature selection and hypothesis generation, while revealing the underlying causal network structure and thus allowing for arbitrary l...

A graph G is called generically minimally rigid in R if, for any choice of sufficiently generic edge lengths, it can be embedded in R in a finite number of distinct ways, modulo rigid transformations. Here, we deal with the problem of determining tight bounds on the number of such embeddings, as a function of the number of vertices. The study of rigid graphs is motivated by numerous application...

In this work, we introduce and study a simple, graph-theoretic model for selfish scheduling among m noncooperative users over a collection of n machines; however, each user is restricted to assign its unsplittable load to one from a pair of machines that are allowed for the user. We model these bounded interactions using an interaction graph, whose vertices and edges are the machines and the us...

The graph G of order n is an L-borderenergetic which means it has the same Laplacian energy as complete Kn. In this paper, we find that combination bipartite graphs and stars can construct infinite numbers classes graphs. We give two Lborderenergetic under operators union, join their mixed. This research could provide experience for further study structural characteristics

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph homomorphisms and mention some results that consider the structure and some parameters of the graphs involved. We discuss vertex transitive graphs and Cayley graphs and their rather fundamental role in some asp...

V1‡ is a declarative visual query language for schema-based property graphs. V1 supports property graphs with mixed (both directed and undirected) edges and half-edges, with multivalued and composite properties, and with empty property values. V1 supports temporal data types, operators, and functions, and can be extended to support additional data types, operators, and functions (one spatiotemp...

Our purpose is to introduce the concept of determining the smallest number of edges of a graph which can be oriented so that the resulting mixed graph has the trivial automorphism group. We find that this number for complete graphs is related to the number of identity oriented trees. For complete bipartite graphs Ks,t, s ≤ t, this number does not always exist. We determine for s ≤ 4 the values ...