For a graph G, its k-rainbow independent domination number, written as γrik(G), is defined the cardinality of minimum set consisting k vertex-disjoint sets V1,V2,…,Vk such that every vertex in V0=V(G)\(∪i=1kVi) has neighbor Vi for all i∈{1,2,…,k}. This invariant was proposed by Kraner Šumenjak, Rall and Tepeh (in Applied Mathematics Computation 333(15), 2018: 353–361), which aims to compute num...

Let R be a commutative ring with identity and M an R-module. In this paper, we associate a graph to M, sayΓ(RM), such that when M=R, Γ(RM) coincide with the zero-divisor graph of R. Many well-known results by D.F. Anderson and P.S. Livingston have been generalized for Γ(RM). We Will show that Γ(RM) is connected withdiam Γ(RM)≤ 3 and if Γ(RM) contains a cycle, then Γ(RM)≤4. We will also show tha...

Most existing tag-based social image search engines present search results as a ranked list of images, which cannot be consumed by users in a natural and intuitive manner. In this demonstration, we present a novel concept-preserving image search results summarization system called prism. prism exploits both visual features and tags of the search results to generate high quality summary, which n...

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

Graphs are high expressive models and especially suitable for modelling highly complex structures, the number of applications that use them for modelling both their data and the processes that manipulate has grown dramatically in recent years. The use of new conceptual structures in real-world applications requires the development of new systems to store and query such structures in order to al...

A core in a graph is usually taken as a set of highly connected vertices. Although general, this definition is intuitive and useful for studying the structure of many real networks. Nevertheless, depending on the problem, different formulations of graph core may be required, leading us to the known concept of generalized core. In this paper we study and further extend the notion of generalized ...

Scene graphs are fundamental data structures for hierarchical scene modeling. The generalized scene graph overcomes various limitations of current scene graph architectures such as support for different 3D rendering systems, integration of multi-pass rendering, and declarative modeling of scenes. The main idea is to separate scene specification from scene evaluation. To specify scenes, scene gr...

This contribution extends generalized LVQ, generalized relevance LVQ, and robust soft LVQ to the graph domain. The proposed approaches are based on the basic learning graph quantization (lgq) algorithm using the orbifold framework. Experiments on three data sets show that the proposed approaches outperform lgq and lgq2.1.