Journal of Algebra Combinatorics Discrete Structures and Applications (JACODESMATH, Yildiz Technical University - YTU)
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Adjacency spectrum and Wiener index of essential ideal graph of a finite commutative ring
Get PDFLet R be a commutative ring with unity. The essential ideal graph ER of R, is a graph with a vertex set consisting of all nonzero proper ideals of R and two vertices I and K are adjacent if and only if I + K is an essential ideal. In this paper, we study the adjacency spectrum of the essential ideal graph of the finite commutative ring Zn, for n = {pm, pm1qm2}, where p, q are distinct primes, and m, m1 , m2 ε N. We show that 0 is an eigenvalue of the adjacency matrix of EZn if and only if either n = p2 or n is not a product of distinct primes. We also determine all the eigenvalues of the adjacency matrix of EZn whenever n is a product of three or four distinct primes. Moreover, we calculate the topological indices, namely the Wiener index and hyper-Wiener index of the essential ideal graph of Zn, for different forms of n
A note on CII groups and CCII groups
Get PDFA group G is CII or, equivalently, 2-Engel if [g, h]= [g^-1;h^-1] for all elements g and h in G, and is CCII if the central quotient G/Z(G) is CII. In this paper, we give sufficient conditions and necessary conditions for a group to be CCII. In particular, we show that every CCII group is nilpotent of class at most 4 and list all CII groups and all CCII groups of order n with n < 64 up to isomorphism
On a variant of k-plane trees
Get PDFIn this paper, we introduce a class of plane trees whose vertices receive labels from the set {1,2,...,k} such that the sum of labels of adjacent vertices does not exceed k+1 and all vertices of label 1 are always on the left of all other vertices. Using generating functions, we enumerate these trees by number of vertices and label of the root, root degree, label of the eldest or youngest child of the root and forests.
 
Construction of (v,k,1) cyclic difference families with small parameters
Get PDFWe construct all nonequivalent (v,k,1) cyclic difference families for 18 sets of parameters v and k for which classification results were not known. We also present the multipliers of all previously classified CDFs with small parameters. Most of the results are double-checked by two different backtrack search algorithms. The usage of an interesting property of the considered objects makes one of these algorithms faster than the other
On generator polynomial matrices of quasi-cyclic codes with linear complementary duals
Get PDFUsing notion of generator polynomial matrices of quasi-cyclic codes, we show a necessary and sufficient condition for which these codes are to be linear complementary dual. This extends the well-known result by Yang and Massey on cyclic codes to quasi-cyclic codes. As an application we present various examples of optimal binary LCD quasi-cyclic codes
The Additive constacyclic codes and the MacWilliams identities over mixed alphabets: MacWilliams identities of additive constacyclic codes
No full textLet be the ring of integers modulo a prime integer , where is a quadratic residue modulo . This paper presents the study of constacyclic codes over chain rings and . We also study additive constacyclic codes over and using the generator polynomials over the rings and respectively. Further, by defining Gray maps on , and we obtain some results on the Gray images of additive codes. Then we provide the weight enumeration and MacWilliams identities corresponding to the additive codes over
On submodule spectrum in multiplication le-modules
Get PDFIn this article, we have studied the Zariski topology related to a submodule element of a le-module. Obtained a base for the complement of the submodule spectrum and topological features, along with some characterizations of the radical of a submodule element, are established. Several algebraic conditions are obtained for an open subset concerning the Zariski topology to become compact, dense, Noetherian, etc
Self-orthogonal and quantum codes over chain rings
Get PDFIn this paper, we investigate the Gray images of codes over chain rings, leading to the derivation of infinite families of self-orthogonal linear codes over the residue field . We determine the parameters of optimal self-orthogonal and divisible linear codes. Additionally, we study the Gray images of quasi-twisted codes, resulting in some self-orthogonal Griesmer quasi-cyclic codes. Finally, we employ the CSS construction to derive some quantum codes based on self-orthogonal linear codes
On energies of graphs with given independence number and families of hyperenergetic graphs
Get PDF Let be a simple graph of order and its line graph.
Then, the iterated line graph of is defined recursively as The energy is the sum of absolute values of the eigenvalues of . In this paper, it is derived a sharp upper bound for the energy of the line graph of a connected graph of order and independence number not less than where . This bound is attained, if and only if, is isomorphic to the complete split graphs . It is also determined a lower bound for the energy of the line graph of a graph of order and independence number . For and , the equality holds, if and only if
As a consequence, families of hyperenergetic graphs are determined.
Also, a lower bound for the energy of the iterated line of a graph of order and independence number is given and, for , the equality holds, if and only if, . Additionally, an upper bound for the incidence energy of connected graphs of order and independence number not less than is presented. Moreover, an upper bound on the Laplacian energy-like of the complement of is presented. For , the bound is attained, if and only if, Finally, a Nordhaus-Gaddum type relation is given
Local and 2-local automorphisms of null-filiform and filiform associative algebras
Get PDFIn the present paper automorphisms, local and 2-local automorphisms of -dimensional null-filiform and filiform associative algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these algebras is clarified. It turns out that the common form of the matrix of an automorphism on these algebras does not coincide with the local automorphism's matrices common form on these algebras. Therefore, these associative algebras have local automorphisms that are not automorphisms.Also, that each 2-local automorphism of null-filiform algebra is an automorphism and some associative filiform algebras admit 2-localautomorphisms which are not automorphisms are proved.
This work was partially supported by RSF 22-71-1000