Knowledge Graphs (KGs) currently contain a vast amount of structured information in the form entities and relations. Because KGs are often constructed automatically by means extraction processes, they may miss that was either not present original source or successfully extracted. As result, might lack useful valuable information. Current approaches aim to complete missing have two main drawback...

Matrix symmetrization and several related problems have an extensive literature, with a recurring ambiguity regarding their complexity status and their relation to graph isomorphism. We present a short survey of these problems to clarify their status. In particular we recall results from the literature showing that matrix symmetrization is in fact NP-hard, while graph isomorphism is still an op...

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

Suppose G = (V,E) is a simple graph and k is a fixed positive integer. A vertex z k-neighborhood-covers an edge (x, y) if d(z, x) ≤ k and d(z, y) ≤ k. A k-neighborhoodcovering set is a set C of vertices such that every edge in E is k-neighborhood-covered by some vertex in C. A k-neighborhood-independent set is a set of edges in which no two distinct edges can be k-neighborhood-covered by the sa...

In this paper, we propose a locality-constrained and sparsity-encouraged manifold fitting approach, aiming at capturing the locally sparse manifold structure into neighborhood graph construction by exploiting a principled optimization model. The proposed model formulates neighborhood graph construction as a sparse coding problem with the locality constraint, therefore achieving simultaneous nei...

In this paper, we explore a variant of the game Cops and Robber introduced by Bonato et al. where robber is invisible unless outside common neighborhood cops. The hyperopic cop number analogous to investigate bounds on quantity. We define small set relate minimum cardinality graph parameter number. consider diameter [Formula: see text] graphs, particularly join two as well Cartesian products.

Let G = (V,E) be a connected graph, An equitable dominating S of a graph G is called the neighborhood connected equitable dominating set (nced-set) if the induced subgraph 〈Ne(S)〉 is connected The minimum cardinality of a nced-set of G is called the neighborhood connected equitable domination number of G and is denoted by γnce(G). In this paper we initiate a study of this parameter. For any gra...

We consider n independent points with a common but arbitrary density fin R a. Two points (X~, Xj) are joined by an edge when a certain set S(X~, Xj) does not contain any other data points. The expected number E(N) of edges in the graph depends upon n, f and the definition of S. Examples include rectangles, spheres and loons; these lead to the graph of all dominance pairs, the Gabriel graph and ...

Graph clustering methods such as spectral clustering are defined for general weighted graphs. In machine learning, however, data often is not given in form of a graph, but in terms of similarity (or distance) values between points. In this case, first a neighborhood graph is constructed using the similarities between the points and then a graph clustering algorithm is applied to this graph. In ...

A 2-rainbow dominating function ( ) of a graph  is a function  from the vertex set  to the set of all subsets of the set  such that for any vertex  with  the condition  is fulfilled, where  is the open neighborhood of . A maximal 2-rainbow dominating function on a graph  is a 2-rainbow dominating function  such that the set is not a dominating set of . The weight of a maximal    is the value . ...