This paper deals with some results concerning the notion of extended ideal based zero divisor graph $overline Gamma_I(R)$ for an ideal $I$ of a commutative ring $R$ and characterize its bipartite graph. Also, we study the properties of an annihilator of $overline Gamma_I(R)$.

A proper vertex coloring of a non oriented graph G = (V, E) is linear if the graph induced by the vertices of two color classes is a forest of paths. A graph G is L-list colorable if for a given list assignment L = {L(v) : v ∈ V }, there exists a proper coloring c of G such that c(v) ∈ L(v) for all v ∈ V . If G is L-list colorable for every list assignment with |L(v)| ≥ k for all v ∈ V , then G...

A graph G = (V, E) is (k, k′)-total weight choosable if the following is true: For any (k, k′)-total list assignment L that assigns to each vertex v a set L(v) of k real numbers as permissible weights, and assigns to each edge e a set L(e) of k′ real numbers as permissible weights, there is a proper L-total weighting, i.e., a mapping f : V ∪ E → R such that f(y) ∈ L(y) for each y ∈ V ∪ E, and f...

Let ρn(V ) be the number of complete hyperbolic manifolds of dimension n with volume less than V . Burger, Gelander, Lubotzky, and Moses[2] showed that when n ≥ 4 there exist a, b > 0 depending on the dimension such that aV logV ≤ log ρn(V ) ≤ bV logV, for V ≫ 0. In this note, we use their methods to bound the number of hyperbolic manifolds with diameter less than d and show that the number gro...

We define a general scheme for the evolution of fragmentation functions which resums soft gluon logarithms in a manner consistent with fixed order evolution. We present an explicit example of our approach in which double logarithms are resummed using the Double Logarithmic Approximation. We show that this scheme reproduces the Modified Leading Logarithm Approximation in certain limits, and find...

This paper deals with (global) finite-gain input/output stabilization of linear systems with saturated controls. For neutrally stable systems, it is shown that the linear feedback law suggested by the passivity approach indeed provides stability, with respect to every L-norm. Explicit bounds on closed-loop gains are obtained, and they are related to the norms for the respective systems without ...

A biclique is a complete bipartite subgraph of a graph. This paper investigates the fractional biclique cover number, bc∗(G), and the fractional biclique partition number, bp∗(G), of a graph G. It is observed that bc∗(G) and bp∗(G) provide lower bounds on the biclique cover and partition numbers respectively, and conditions for equality are given. It is also shown that bc∗(G) is a better lower ...

The electromagnetically induced transparency (EIT) phenomenon in a four level atomic system with tripod configuration is studied. The results show that this configuration is equivalent to the combination of two single three-level Λ configurations, which, under certain conditions, results in the so-called double-EIT (DEIT) phenomenon. The properties of the double transparency windows for DEIT ar...

We investigate the push-relabel algorithm for solving the problem of finding a maximum cardinality matching in a bipartite graph in the context of the maximum transversal problem. We describe in detail an optimized yet easy-to-implement version of the algorithm and fine-tune its parameters. We also introduce new performance-enhancing techniques. On a wide range of real-world instances, we compa...

We consider the bipartite version of the degree/diameter problem, namely, given natural numbers ∆ ≥ 2 and D ≥ 2, find the maximum number Nb(∆,D) of vertices in a bipartite graph of maximum degree ∆ and diameter D. In this context, the Moore bipartite bound Mb(∆,D) represents an upper bound for Nb(∆,D). Bipartite graphs of maximum degree ∆, diameter D and order Mb(∆,D), called Moore bipartite gr...