Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Stopping sets of codes from complete bipartite graph 87 97 12564 10.22061/jdma.2025.11781.1115 EN Hamidreza Maimani Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Iran Mahbubeh Nazari Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran. Abolfazl Tehranian Department of Mathematics, Science and Research Branch, Islamic Azad university, Tehran, Iran. Journal Article 2025 02 23 Let C be a code with parity-check matrix H. A stopping set S of size l ≤ n for H is an l-columns submatrix of Hs of H which does not contain a row with weight one. In this paper we consider the code which parity-check is incidence matrix of complete bipartite graph Km,n. These codes are LDPC codes and we obtain the stopping sets for these codes.

https://jdma.sru.ac.ir/article_12564_f6ca2b6c40393449f82c5e4fec61bdfb.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Complementary distance Seidel equienergetic graphs 99 106 12569 10.22061/jdma.2025.12527.1165 EN Indulal G Gopalapillai Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India Deena Scaria Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India Jinu Mary Department of Mathematics, Mar Thoma College, Tiruvalla, Pathanamthitta-689103, India Journal Article 2025 09 18 The distance matrix, its eigenvalues, and the corresponding distance energy of a connected graph have been extensively studied in the literature. However, research on the Distance Seidel matrix associated with a connected graph remains in its developmental stages. The Distance Seidel matrix of a graph yields the Distance Seidel eigenvalues ∂1S ≥ ∂2S ≥ … , ∂nS, which together constitute the Distance Seidel spectrum of G. In [1], the authors introduced the complementary distance matrix and studied its properties. Motivated by these we introduce the complementary distance seidel matrix of a connected graph and obtain some results for some classes of graphs. In this paper, we investigate the Complementary Distance Seidel Spectrum of complement of line graphs of regular graphs.

https://jdma.sru.ac.ir/article_12569_eb190aba550879c058fa77c9e88838ad.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Cayley graphs and G-graphs of gyro-groups 107 122 12565 10.22061/jdma.2025.12144.1138 EN Gholam Hossein Fath-Tabar Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. R. Iran; Neda Moradi Department of Mathematics, Statistics and Computer Science, Faculty of Science, University of Kashan, Kashan 87317-51167, I. Alain Bretto Universite de Caen, GREYC CNRS UMR-6072, Campus II Bd Marechal Juin BP 5186, 14032 Caen cedex Caen, France Journal Article 2025 06 07 The present paper investigates the structural properties of Cayley graphs and G-graphs associated with certain gyro-groups, providing rigorous proofs for several key characteristics. Additionally, we conduct a comprehensive review of specific classes of gyro-groups, including gyro-commutative gyro-groups, dihedral gyro-groups, and dihedralized gyro-groups. Subsequently, we derive and establish significant properties of the corresponding G-graphs. The study culminates in an examination of the symmetry properties exhibited by the Cayley graphs and G-graphs of selected gyro-groups, contributing to a deeper understanding of their algebraic and combinatorial structures.

https://jdma.sru.ac.ir/article_12565_cb75dd11e67d4a7a422498a33c057131.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 On MLDR and MHDR codes 123 129 12566 10.22061/jdma.2025.12537.1167 EN Farzaneh Farhang Baftani Department of Mathematics, Ard.C, Islamic Azad University Journal Article 2025 09 21 For a code D of length l over ℤ4, we denote by M(D) the matrix containing all code words of D on its rows. Any columns of M(D) corresponds to the column which is zero or it has zero and 2 equally or it has all elements of ℤ4 equally. The Lee Weight for these columns is defined 0, 2 and 1, respectively. If we calculate the sum of all Lee weights of columns of M(D), it is denoted by wtL(D) and called the Lee Support Weight of D. In addition, the m-th Generalized Lee Weight (GLW) for D, denoted by dmL(D), is defined as the minimum of the Lee Support Weights of all submodules of D of rank m. In other words, dmL(D) = min{wtL(E) ; E is a ℤ4-submodule of D, rank(E) = m}. It is obtained that for m, 1 ≤ m ≤ rank(D), we have ⌊(dmL(D) - 2m + 1) / 2⌋ ≤ l - rank(D). The code which meets the recent upper bound is called Maximum Lee Distance separable with respect to Rank (m-th MLDR) code. Also, if dmH(D) denotes the m-th GHW for code D, it is defined as dmH(D) = min{|supp(E)| ; E is a ℤ4-submodule of D and rank(E) = m}. The upper bound for dmH(D) is l - rank(D). The code meeting this upper bound is called MHDR code. In this paper, we investigate MLDR codes, MHDR codes and relation between them, in detail.

https://jdma.sru.ac.ir/article_12566_c63d7d7a0f6532ce85c9388e6d26ea0d.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Graph‑enhanced fraud detection in health insurance: integrating centrality metrics and community analysis for improved accuracy 131 151 12567 10.22061/jdma.2026.12810.1181 EN Mohammad Mahdi Ahmadi Department of Engineering Sciences, University of Tehran, Tehran, I. R. Iran Asma Hamzeh Department of Modern Insurance Technologies, Insurance Research Center, Tehran, I. R. Iran Ali Kamandi Department of Engineering Sciences, University of Tehran, Tehran, I. R. Iran Journal Article 2025 12 11 The dynamic nature of fraud and the emergence of new fraudulent methods in the insurance industry, along with the insufficient capability of insurance companies to prevent, identify, and combat it, may lead insurance companies toward bankruptcy in the not-too-distant future. Given that insurance companies serve as the main entity providing insurance services and compensating losses, their significant role in preventing and detecting fraud makes the various strategies they employ to counter fraud significant. In the current situation, identifying and analyzing the phenomenon of fraud, which leads to increased costs in the insurance industry, appears to be essential for controlling factors and ensuring the survival of insurance companies. This article examines the use of graph theory for fraud detection in the health insurance industry. By extracting information from relevant databases and constructing a comprehensive network graph, existing patterns are analyzed and suspicious fraudulent cases are identified. The proposed method was implemented on real data, and the results showed that this method is capable of detecting fraud with 95% accuracy, which is an improvement over the existing method. All implementation codes and supplementary materials are openly available on GitHub [https://github.com/MohammadMehdi41/fraudDetection.git].

https://jdma.sru.ac.ir/article_12567_88efd2df65b528f27f5c7e4f744c5bb4.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Finite groups whose enhanced power graphs are unique 153 161 12568 10.22061/jdma.2026.12605.1171 EN Mahsa Mirzargar Faculty of Science, Mahallat Institute of Higher Education, Mahallat, I. R. Iran Journal Article 2025 10 10 The enhanced power graph Pe(G) of a group G is the graph whose vertex set is G, with two elements u and v adjacent if there is an element z ∈ G such that ⟨u, v⟩ = ⟨z⟩. In this paper, we investigate classes of groups whose enhanced power graphs uniquely determine their structure; that is, if Pe(G) ≅ Pe(H), then G ≅ H. We also study the set of natural numbers n for which every group of order n is uniquely determined (up to isomorphism) by its enhanced power graph. We consider groups that have the same number of elements of each order and exploit necessary conditions to identify situations in which a property of a group G is preserved by all groups sharing the same enhanced power graph. In particular, we show that if two finite groups have isomorphic enhanced power graphs and one of them is nilpotent or has a normal Hall subgroup, then the other must also share that property.

https://jdma.sru.ac.ir/article_12568_8c665163ee23ba68c10117a4f50d2d2e.pdf