In many real world problems, data sometimes comes from n agents (n≥2), multipolar information exists. For issues that are associated with uncertainty, this information can not be showed with the values of crisp, fuzzy, intuitionistic or bipolar. Graph is one of the mathematical models widely used in different sciences. Ambiguity in a graph where data depends on the n parameter can not be showed...

A graph G is called fractional [a,b]-covered if for every edge e of there a [a,b]-factor with the indicator function h such that h(e)=1. In this paper, we provide tight spectral radius condition graphs being [a,b]-covered.

Let FG(P ) be a functional defined on the set of all the probability distributions on the vertex set of a graph G. We say that G is symmetric with respect to FG(P ) if the uniform distribution on V (G) maximizes FG(P ). Using the combinatorial definition of the entropy of a graph in terms of its vertex packing polytope and the relationship between the graph entropy and fractional chromatic numb...

The linear complementarity problem is a continuous optimization problem that generalizes convex quadratic programming, Nash equilibria of bimatrix games and several such problems. This paper presents a continuous optimization formulation for the weighted independence number of a graph by characterizing it as the maximum weighted l1 norm over the solution set of a linear complementarity problem ...

This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper. Topics covered in this paper include: (1)What is a Smarandache System? (2)Vertex-Edge Labeled Graphs with Applications: (i)Smarandachely k-constrained labeling of a grap...

The EU-funded project Lynx focuses on the creation of a knowledge graph for legal domain (Legal Knowledge Graph, LKG) and its use semantic processing, analysis enrichment documents from domain. This article describes cases covered in project, entire developed platform services that operate documents.

We give a very simple proof that every non-bipartite matching covered graph contains a nice subgraph that is an odd subdivision of K 4 or C 6. It follows immediately that every brick diierent from K 4 and C 6 has an edge whose removal preserves the matching covered property. These are classical and very useful results due to Lovv asz.