Let F be a finite field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n× n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with pt elements, p = 2, it is shown that mr(F,G) ≤ 2 if and only if the compl...

Let F be a finite field, G = (V, E) be an undirected graph on n vertices, and let S(F,G) be the set of all symmetric n× n matrices over F whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. Let mr(F,G) be the minimum rank of all matrices in S(F,G). If F is a finite field with pt elements, p = 2, it is shown that mr(F,G) ≤ 2 if and only if the compl...

Strongly perfect graphs were introduced by C. Berge and P. Duchet in [1]. In [4], [3] the following was studied: the problem of strong perfectness for the Cartesian product, the tensor product, the symmetrical difference of n, n ≥ 2, graphs and for the generalized Cartesian product of graphs. Co-strong perfectness was first studied by G. Ravindra and D. Basavayya [5]. In this paper we discuss s...

A graph is called well-covered if every maximal independent set of vertices of G is a maximum independent set; recall that S is independent if no two of its vertices are adjacent. In this paper we define the concept of well-covered by monochromatic paths graphs which is a variation of well-covered graphs. We consider some classical constructions of graphs: G-join of graphs and duplication of a ...

Graphs can be found in applications like social networks, bibliographic networks, and biological databases. Understanding the relationship, or links, among graph nodes enables applications such as link prediction, recommendation, and spam detection. In this paper, we propose link-based similarity join (LS-join), which extends the similarity join operator to link-based measures. Given two sets o...

The paper presents an iterative version of join-tree clustering that applies the message passing of join-tree clustering algorithm to join-graphs rather than to join-trees, iteratively. It is inspired by the success of Pearl’s belief propagation algorithm (BP) as an iterative approximation scheme on one hand, and by a recently introduced mini-clustering (MC(i)) success as an anytime approximati...

Shema-free SQL takes into consideration two relaxations 1. Schema Relaxation: Users need not have to specify the exact name of the tables and attributes • Join Path: users need not have to specify the join path in the query Reducing user workload of writing SQL queries and knowing the complete database schema to query the RDBMS in order to get desired results Generation of Join Network (Interpr...