Journal of Algebra Combinatorics Discrete Structures and Applications (JACODESMATH, Yildiz Technical University - YTU)
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Unit Regular Graphs over Finite Rings
Full text linkThis paper introduces the concept of a unit regular graph over any given ring. The unit regular graph is a simple undirected graph, where its vertices correspond to elements of the ring. Two vertices are connected if their sum results in a unit regular element within the ring. The research explores various aspects of this graph, such as completeness, vertex degrees, Eulerian and Hamiltonian properties, girth, matching number, clique number, and independence number. Furthermore, the study delves into specific properties of these graphs for certain ring types
On Albertson spectral properties of graphs with self-loops
Full text linkThe Albertson irregularity measure is defined as In this work, the concept of Albertson energy is extended from simple graphs to graphs with self-loops. Also the expression for the Albertson eigenvalues of a graph with self-loops are given. Some bounds on the Albertson energy of graphs with self-loops and the spread of are obtained. In the last section, the Albertson energy of complete, complete bipartite, crown and thorn graphs with self-loops are computed
Combinatorial properties of certain Toeplitz matrices
Full text linkIn additive combinatorics, a family of finite sets is said to have bounded doubling if there exists a uniform constant such that |A_i + A_i|< K|A_i| for all i. In this paper, we study such families in the context of certain symmetric Toeplitz matrices over a field F. In particular, we show that if each matrix has bandwidth b and diagonal entries chosen from a finite set , then the resulting family admits a doubling constant that depends only on b and the additive properties of , but is independent of the matrix dimension. Also, if the diagonals lie in the image of a fixed-dimensional linear map , then the doubling constant depends on m rather than b. We include examples to illustrate how one-dimensional constraints on S lead to especially small doubling constants
On weakly S-2-absorbing filters of lattices
Full text linkLet £ be a bounded distributive lattice and S a join closed subset of £. Following the concept of weakly S-2-absorbing submodules, we define weakly S-2-absorbing filters of £. We will make an intensive investigate the basic properties and possible structures of these filters
Totally projective QTAG-modules and generalizations
Full text linkIn this project, we prioritize our study on some types of generalized torsion abelian groups. The torsion abelian group is an important tool in the theory of modules. Analogous to this concept, we study the totally projective modules and discuss its relation with isotype as well as separable submodules. One of the main purposes of the present paper is to give a necessary and sufficient condition for an isotype submodule of a totally projective module to be itself a totally projective module
Valuation overrings of polynomial rings and group of divisibility
Full text linkIn this work, we discuss the types of valuation overrings of based on the rank and rational rank of value groups. Also, we describe the group of divisibility of a finite intersection of valuation overrings of In particular, we focus on the case for $n > 3.
-Generalized monomial codes
No full textIn this paper we generalize cyclic codes to another more large linear codes, that is -monomial codes. It is shown that for a -monomial code, its Euclidean and -Galois dual is also -monomial code. Furthermore we present the equivalence between -monomial codes and generalized monomial codes. By considering the skew polynomial ring, we show that -monomial codes can relate to submodules under a condition and to ideals under other condition,this allow us to give a characterization of -monomial codes. More results on the -Galois dual of -monomial codes are given with additional properties on self duality and self orthogonality. The Generalized -monomial codes are discussed with their algebraic structure. The paper is closed by the investigation of the algebraic structure of -monomial codes over the ring where .  
On the three graph invariants related to matching of finite simple graphs
Full text linkLet G be a finite simple graph on the vertex set V(G) and let ind-match(G), min-match(G) and match(G) denote the induced matching number, the minimum matching number and the matching number of G, respectively. It is known that the inequalities ind-match(G) <= min-match(G) <= match(G) <= 2min-match(G) and match(G) <= |V(G)|/2 hold in general.
In the present paper, we determine the possible tuples (p, q, r, n) with ind-match(G) = p, min-match(G) = q, match(G) = r and |V(G)| = n arising from connected simple graphs. As an application of this result, we also determine the possible tuples (p`, q, r, n) with reg(G) = p`, min-match(G) = q, match(G) = r and |V(G)| = n arising from connected simple graphs, where I(G) is the edge ideal of G and reg(G) = reg(K[V(G)]/I(G)) is the Castelnuovo--Mumford regualrity of the quotient ring K[V(G)]/I(G). 
New Results and Bounds on Codes over GF(19)
Full text linkExplicit construction of linear codes over finite fields is one of the most important and challenging problems in coding theory. Due to the centrality of this problem, databases of best-known linear codes (BKLCs) over small finite fields have been available. Recently, new databases for BKLCs over larger alphabets have been introduced. In this work, a new database of BKLCs over the field GF(19) is introduced, containing lower and upper bounds on the minimum distances for codes with lengths up to 150 and dimensions between 3 and 6. Computer searches were conducted on cyclic, constacyclic, quasi-cyclic, and quasi-twisted codes to establish lower bounds. These searches resulted in many new linear codes over GF(19)
A note on injective dimension of local cohomology modules
Full text linkIn this study, we assume that R is a commutative Noetherian ring with nonzero identity. We present upper bounds for the injective dimension of I, where I is any ideal in the ring R, in terms of the injective dimension of its local cohomology modules and an upper bound for the injective dimension that involves the theory of local cohomology modules. Since I is an ideal in R, we obtain applications of the theory in a general context