A. Dilek Güngör

On the distance spectral radius and the distance energy of graphs

The D-eigenvalues {μ1, μ2, … , μ p } of a connected graph G are the eigenvalues of its distance matrix D. The D-energy of a graph G is the sum of the absolute values of its D-eigenvalues denoted by E D (G). In this article, we obtain a lower bound for the largest D-eigenvalue of G and an upper bound for E D (G) which improve Indulals bounds [G. Indulal, Sharp bounds on the distance spectral radius and the distance energy of graphs, Linear Algebra Appl. 430 (2009), pp. 106–113]. In the final section of the article, we give an important remark on the distance regular graphs.

Improved upper and lower bounds for the spectral radius of digraphs

Let G be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius @r(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, sharp upper and lower bounds on @r(G) are given. We show that some known bounds can be obtained from our bounds.

A New Like Quantity Based on "Estrada Index"

We first define a new Laplacian spectrum based on Estrada index, namely, Laplacian Estrada-like invariant, LEEL, and two new Estrada index-like quantities, denoted by S and , respectively, that are generalized versions of the Estrada index. After that, we obtain some lower and upper bounds for LEEL, S, and .

On the Norms of Toeplitz and Hankel Matrices with Pell Numbers

Let us define A = [a ij ] i,i = 0 n-1 and B = [b ij ] i,i = 0 n-1 as n×n Toeplitz and Hankel matrices, respectively, such that a ij = P i−j and b ij = P i+j , where P denotes the Pell number. We present upper and lower bounds for the spectral norms of these matrices.

A New Example of Deficiency One Groups

The main purpose of this paper is to present a new example of deficiency one groups by considering the split extension of a finite cyclic group by a free abelian group having rank two.

Primes in Z[exp(2πi/3)]

In this paper, we study the primes in the ring Z[w], where w = exp(2πi/3) is a cubic root of unity. We gave a classification of them and some results related to the use of them in the calculation of cubic residues are obtained.

On the Efficiency of Semi‐Direct Products of Finite Cyclic Monoids by One‐Relator Monoids

In this paper we give necessary and sufficient conditions for the efficiency of a standard presentation for the semi‐direct product of finite cyclic monoids by one‐relator monoids.

Generalization for Estrada Index

In this paper the Estrada index of Hermite matrix is firstly defined and investigated. In fact this is a natural generalization of Estrada, distance Estrada and Laplacian Estrada indices. Thus all properties about them can be handled by this new index.

A NEW EXAMPLE FOR MINIMALITY OF MONOIDS

By considering the split extension of a free abelian monoid having finite rank by a finite monogenic monoid, the main purposes of this paper are to present examples of efficient monoids and, also, minimal but inefficient monoids. Although results presented in this paper seem as in the branch of pure mathematics, they are actually related to applications of Combinatorial and Geometric Group-Semigroup Theory, especially computer science, network systems, cryptography and physics etc., which will not be handled here.