Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 On mixed double Roman domination number and 2-independence number of graphs 163 175 12615 10.22061/jdma.2026.12594.1170 EN Halimeh Koulivand Department of Mathematics, Tafresh University, Tafresh, Iran. Mohammad Habibi Tafresh University Hassan Arianpoor Department of Mathematics, Tafresh University, Tafresh, Iran. Mina Valinavaz Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran. Journal Article 2025 10 05 Let G=(V(G),E(G)) be a simple graph. A mixed double Roman dominating function (MDRDF) on G is a function f:V(G)∪E(G) → {0,1,2,3} such that (i) if f(u)=0, then u has at least two neighbors assigned 2 under f or one neighbor w with f(w)=3; (ii) if f(u)=1, then u must have at least one neighbor w with f(w)≥ 2. The weight of f is equal to Σu∈V(G)∪E(G)f(u). The mixed double Roman domination number γdR*(G) is the minimum weight among all MDRDF's of G. A subset X of V(G) is a 2-independent set of G if the subgraph induced by the vertices of X is isomorphic to rK2∪sK1, where 2r+s=|X|. The maximum cardinality of a 2-independent set of G is the 2-independence number β2(G). In this paper, it is shown that these parameters are incomparable, in general. Also, we prove that either T is a path or a tree with a quasi-diagonal path u1,…, uk such that d(u2)≠ 2 or d(u3)≠ 2, then γdR*(T)≤ 2β2(T). Moreover, all extremal trees in this family that attaining equality are characterized.

https://jdma.sru.ac.ir/article_12615_4e8e6b52afed03c1349c984d71037b0f.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 Efficient protocols for group key establishment based on secret sharing 177 191 12616 10.22061/jdma.2025.12734.1178 EN Mahnaz Noroozi Department of Computer Science, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran. 0000-0002-3021-438X Maryam Ahmadi Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran Journal Article 2025 11 23 Secure group communication is a fundamental requirement in modern distributed systems, relying on efficient and secure group key establishment protocols. While secret sharing has been effectively utilized to construct such protocols, existing approaches often incur significant computational overhead. This paper addresses this efficiency challenge by presenting novel improvements to the group key agreement protocol of Harn and Lin and the group key distribution protocol of Harn and Hsu. Our key insight is to replace the use of Shamir's (n,n) threshold secret sharing scheme in the existing protocols with Shamir's (2,2) threshold scheme, which consequently reduces the core polynomial operations from degree n to degree one. This optimization drastically lowers the computational cost associated with polynomial construction and interpolation, while maintaining the security guarantees of the original protocols. Security analysis demonstrates that the proposed protocols provably satisfy essential properties such as key confidentiality, authenticity, and forward secrecy under the hardness of the decisional Diffie-Hellman problem. Performance comparisons confirm that our constructions achieve superior efficiency in both computation and communication, making them highly practical for large-scale group applications.

https://jdma.sru.ac.ir/article_12616_7a1e5a8528c026edbfab6baa906f621f.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 Proof of a conjecture for the watching number 193 198 12617 10.22061/jdma.2026.12640.1177 EN ‎Ebrahim Vatandoost ‎Department of Basic Science, ‎Imam Khomeini International University‎‎,‎Qazvin‎, ‎Iran ‎Ahmad Abbasi ‎Department of Pure Mathematics, ‎Faculty of Mathematical Sciences‎, ‎University of Guilan‎‎, ‎Rasht‎, ‎Iran Kamran Mirasheh Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran Journal Article 2025 10 22 In this paper, we prove that for every connected graph G of order n, the watching number of its subdivision graph S(G) is exactly n. This result confirms a conjecture previously proposed by Vatandoost et al. [7].

https://jdma.sru.ac.ir/article_12617_1c6baa190352de512d95e912680bf17d.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 A bibliometric review of the Journal of Discrete Mathematics and Applications (2011–2025) 199 220 12611 10.22061/jdma.2026.12996.1190 EN Sara Gheisari Goudarzi Shahid Rajaee Teacher Training University Journal Article 2026 02 23 This study evaluates the knowledge structure and thematic development of the Journal of Discrete Mathematics and Applications (JDMA) from 2011 to 2025, aiming to clarify the journal’s development trajectory and identify strategic opportunities through a bibliometric analysis of 121 documents using R and VOSviewer. The analysis finds that JDMA exhibits a 6.98% annual growth, indicating robust scientific development. Keyword co-occurrence and author network analyses show a concentration on topological indices and molecular graphs. Key authors such as Mojtaba Ghorbani and Gutman play central roles as connectors, advancing the international exchange of scientific ideas. Expanding international collaborations and diversifying research themes, especially in graphs and hypergraphs, are crucial for enhancing JDMA's global standing. Recommendations include supporting established authors in building international networks, organizing joint special issues, and broadening thematic coverage in emerging topics—measures that could strengthen the journal’s international scientific impact.

https://jdma.sru.ac.ir/article_12611_bbe6592371497913bf49ec26ff607f02.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 On the general ‎ABC-spectral radius and ABC-energy of a graph 221 233 12618 10.22061/jdma.2026.12740.1182 EN Kianoosh Hayati Department of Mathematics, Faculty of Science, Razi University, Kermanshah, Iran Farzad Shaveisi Department of Mathematics, Faculty of Science Kermanshah, 6714967346, Iran 0000-0001-9138-6321 Journal Article 2025 12 12 Let G be a simple graph with vertex set {v1, v2,…, vn} where di denotes the degree of vi. For every real number α, the generalized ABC-matrix of G, denoted by Ωα=[ωαij] is an n×n matrix such that ωαij=((di + dj - 2)/didj)α if vivj is an edge and ωαij=0, otherwise. In this paper, some bounds for the spectral radius of Ωα are found. Among other results, some bounds for the generalized ABC-energy are determined in terms of generalized ABC-index and general Randić index.

https://jdma.sru.ac.ir/article_12618_1cbac41f934011d788440f0392b21284.pdf

Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 3 2026 09 01 Binary codes from uniform subset graph G(n, 4, i) 235 246 12619 10.22061/jdma.2026.12830.1183 EN Abolfazl Bahmani Department of Mathematics, University of Zanjan Zanjan, Iran. Mojgan Emami Department of Mathematics,University of Zanjan, Zanjan, Iran Journal Article 2025 12 17 Let Ω be a set of cardinality n with n ≥ 8, and let V = P4(Ω) denote the family of all 4-element subsets of Ω. For i = 0, 1, 2, 3, let G(n,4,i) be the graph with vertex set V, where two vertices are adjacent precisely when their intersection has cardinality i. This graph is referred to as the uniform subset graph. We denote the adjacency matrix of G(n,4,i) by Ai(n). In this work, we investigate the binary codes Ci(n) arising from the row space of Ai(n), determine their parameters, and establish the relationships between Ci(n) and Cj(n)⊥ for i,j ∈ {0,1,2,3}.

https://jdma.sru.ac.ir/article_12619_4a5b420cdba45f72f3c51fadc06f224f.pdf