Dr. Roopa. B

@srmist.edu.in

Assistant Professor and Department of Mathematics
SRM Institute of Science and Technology, Ramapuram campus

Dr. Roopa. B


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https://researchid.co/rooparb

RESEARCH INTERESTS

Graph Theory and Cryptography
9

Scopus Publications

Scopus Publications

  • Exploring the Dynamics of Modular Multiplicative Divisor Labeling in Interconnected Cycle Graph Gangs
    P. Kalarani, R. Revathi, R. Vijaykrishnaraj, V G Smilin Shali, B. Kalaiselvi, B. Roopa
    2026 6th International Conference on Advances in Electrical Computing Communications and Sustainable Technologies Icaect 2026, 2026
    This study investigates Modular Multiplicative Divisor (MMD) labeling in gangs of cycle graphs, a structure that has been largely unexplored in graph theory. The work aims to identify optimal labeling configurations that satisfy MMD criteria while examining the structural and labeling characteristics of interconnected cycle graphs. A systematic framework is developed for assigning vertex and edge labels, ensuring consistency through modular validation. The proposed approach addresses unresolved issues in MMD labeling and extends its theoretical foundation within combinatorial graph theory. Verified through illustrative examples, the results confirm the existence and reliability of MMD labeling in gangs of cycle graphs and provide valuable insights for further research on complex graph structures.
  • Investigating the Use of M-Polynomial for Calculating Topological Indices in Carbazole Dendrimers
    A. Venkatesan, R. Binthiya, B. Roopa, A. Jeslet Kani Bala
    Mathematics and Statistics, 2025
    Graph theory plays an essential role in analysing the structural characteristics of molecular structures and network systems. Among the various degree-based topological indices, the Hyper Zagreb index, Redefined Zagreb index, and Reciprocal Randic index are particularly important for evaluating molecular graphs. I investigated the M-polynomial as a tool for calculating the Hyper Zagreb index, Redefined Zagreb index, and Reciprocal Randic index. Carbazole dendrimers are highly branched macromolecular structures consisting of a central carbazole unit with multiple dendritic branches extending from it. We successfully determined the M-polynomials for Carbozole dendrimers. Furthermore, by leveraging these M-polynomials, we will be computing various topological indices based on degree. Additionally, we obtained the Topological Indices values of Carbozole dendrimers for generations <img src=image/13441196_01.gif> using the M-polynomial. The M-polynomial is firstly used and is determined as follows: <img src=image/13441196_02.gif>. Where <img src=image/13441196_03.gif> and <img src=image/13441196_04.gif> is the total number of edges <img src=image/13441196_05.gif>, where <img src=image/13441196_06.gif>. The theory of Quantitative Structure-Property Relationships (QSPR) is founded on the principle that a compound's physicochemical properties are intrinsically linked to its molecular structure. The results of this study provide a thorough framework for examining dendritic structures using M-polynomials, which adds to the expanding collection of work on molecular graph theory. These findings might help develop prediction models for quantitative structure–property relationship (QSPR) research, especially when it comes to comprehending the physiochemical characteristics of dendritic molecules.
  • Antimagic Labeling of Bi-Star Graphs for Secure and Efficient Cryptographic Data Transformation
    B. Roopa, J. Saral, R. Senthamizh Selvi, R. Binthiya
    International Journal for Global Academic and Scientific Research, 2025
    Graph labeling is a fundamental concept in graph theory with applications in networks, cryptography, and data security. Graph-based cryptographic models and ECC-based methods provide partial solutions but individually face limitations in randomness, computational efficiency, and scalability. Existing graph-based encryption approaches often rely on classical ciphers, have high computational overhead, and offer limited resistance to sophisticated attacks. These gaps highlight the need for a hybrid, efficient, and high-entropy cryptographic framework. This research introduces a novel Bi-Star + ECC encryption scheme that combines super-edge antimagic total labeling of Bi-Star graphs with Elliptic Curve Cryptography (ECC). Plaintext is first converted into a numerical matrix and mapped onto a Bi-Star graph. Unique labels are assigned to vertices and edges, and edge weights are computed as the sum of connected labels, producing ciphertext with distinct, unpredictable values. ECC integration provides key exchange, hybrid encryption, and robust asymmetric security. The process involves mapping input data to a matrix, constructing a weighted Bi-Star graph, calculating unique edge sums, encrypting with ECC, and decoding by reversing the labeling process. This research is implemented on the Python platform. Performance evaluation demonstrates high efficiency and security: encryption/decryption in 2–18 ms, memory usage 1.2–7.2 MB, and security metrics (Confidentiality = 11, Integrity = 10, Security = 10). The method ensures high entropy, low redundancy, and robust resistance against attacks. Integrating Bi-Star graph labeling with ECC provides a secure, efficient, and practical cryptographic mechanism, addressing the limitations of prior graph-based and ECC-only approaches while enabling scalable and high-performance encryption.
  • VisionGrip: Revolutionizing Motor Functionality in Carpal Tunnel Syndrome and Radial Nerve Palsy Patients Through EOG-Controlled Robotic Claw
    G. NirmalaPriya, M. E. Paramasivam, S. Prema, B. Roopa
    Lecture Notes in Electrical Engineering, 2025
  • Innovative Generalization Strategies for the Development of Neutrosophic Sets and Systems
    B. Kalaiselvi, K. Sivakumar, B. Roopa, P. Kalarani, B. Parimalagandhi, K. Kalaimathi
    Proceedings of International Conference on Sustainable Communication Networks and Application Icscn 2025, 2025
    This work introduces advanced generalization techniques for neutrosophic sets and systems, emphasizing mathematical applications to real-time data. Three methods are proposed: Neutrosophic Linear Regression (NLR), Multi-Objective Neutrosophic Optimization (MONO), and the Generalized Neutrosophic Clustering Algorithm (GNCA). NLR extends classical regression to handle missing, inconsistent, and indeterminate values, achieving 92.3% prediction accuracy—12% higher than traditional models. MONO employs neutrosophic membership and indeterminacy functions to optimize decision-making in tasks such as risk assessment and resource allocation, reducing computation time by 20% and improving accuracy by 15%. GNCA effectively groups noisy and uncertain data from domains like finance and climate studies, attaining an F1-score of 89.8%, precision of 90.9%, and recall of 88.8%. Experiments on stock market, climate change, and healthcare datasets validate the methods’ efficiency. Results show that generalized neutrosophic techniques significantly enhance uncertainty handling, data modeling, and decision-making, offering robust solutions for complex real-world problems.
  • Data Encryption Using Face Antimagic Labeling and Hill Cipher
    B. Vasuki, L. Shobana, B. Roopa
    Mathematics and Statistics, 2022
    An approach to encrypt and decrypt messages is obtained by relating the concepts of graph labeling and cryptography. Among the various types of labelings given in [3], our interest is on face antimagic labeling introduced by Mirka Miller in 2003 [1]. Baca [2] defines a connected plane graph <img src=image/13426646_01.gif> with edge set <img src=image/13426646_02.gif> and face set <img src=image/13426646_03.gif> as <img src=image/13426646_04.gif> face antimagic if there exist positive integers <img src=image/13426646_05.gif> and <img src=image/13426646_06.gif> and a bijection <img src=image/13426646_07.gif> such that the induced mapping <img src=image/13426646_08.gif>, where for a face <img src=image/13426646_09.gif>, <img src=image/13426646_10.gif> is the sum of all <img src=image/13426646_11.gif> for all edges <img src=image/13426646_12.gif> surrounding <img src=image/13426646_09.gif> is also a bijection. In cryptography there are many cryptosystems such as affine cipher, Hill cipher, RSA, knapsack and so on. Amongst these, Hill cipher is chosen for our encryption and decryption. In Hill cipher [8], plaintext letters are grouped into two-letter blocks, with a dummy letter X inserted at the end if needed to make all blocks of the same length, and then replace each letter with its respective ordinal number. Each plaintext block <img src=image/13426646_13.gif> is then replaced by a numeric ciphertext block <img src=image/13426646_14.gif>, where <img src=image/13426646_15.gif> and <img src=image/13426646_16.gif> are different linear combinations of <img src=image/13426646_17.gif> and <img src=image/13426646_18.gif> modulo 26: <img src=image/13426646_19.gif> (mod 26) and <img src=image/13426646_20.gif> (mod 26) with condition as <img src=image/13426646_21.gif> is one. Each number is translated into a cipher text letter which results in cipher text. In this paper, face antimagic labeling on double duplication of graphs along with Hill cipher is used to encrypt and decrypt the message.
  • On face bimagic labeling for duplication and double duplication graphs
    B. Roopa, L. Shobana
    Aip Conference Proceedings, 2019
    In this paper, the existence of face bimagic labeling for strong face of duplication of every vertex by an edge of Tree Tn:n≥2 of types (1,0,1), (1,1,0) and (0,1,1), strong face of duplication of every edge by vertex of Tree Tn:n≥2 of type (0,1,1), strong face of duplication of every vertex by an edge of a Cycle graph Cn:n≡1(mod 2), n≥3 of types (1,0,1), (1,1,0) and (0,1,1), and strong face of duplication of every edge by vertex of path graph Pn:n≥2 of types (1,0,1), (1,1,0) and (0,1,1) are proved. Also, we proved the occurance of face bimagic labeling for double duplication of all vertices by edges, DDVV(Pn):n≥2 of types (1,0,1), (1,1,0) and (0,1,1).
  • On face magic labeling of duplication of a tree
    Applied Mathematics and Information Sciences, 2019
  • Face magic labeling for double duplication of cycle related graphs
    Journal of Advanced Research in Dynamical and Control Systems, 2018