Local antimagic vertex coloring of a Myceilski of graphs A. Sethukkarasi, S. Vidyanandini, Soumya Ranjan Nayak Journal of Discrete Mathematical Sciences and Cryptography, 2024 This paper presents an investigation into the fundamental properties associated with the chromatic mean and variance within specific standard graphs, alongside the application of the Mycielski transformation to select graph structures. Furthermore, our study delves into the practical implications of local antimagic vertex coloring, emphasizing its significance in the fields of network security and anomaly detection.
Square difference labeling and co-secure domination in middle graph of certain graphs G. Sarmitha, S. Vidyanandini, Soumya Ranjan Nayak Journal of Discrete Mathematical Sciences and Cryptography, 2024 This paper focus on the dynamic and quickly developing subject of graph Domination study. In this paper, Co-Secure Domination and Square diffrence Labeling for Middle graph of Paths and Regular Spider Graphs has been determined. The findings can be applied on protection strategy for a various communication and interconnection networks, where the routing servers as the network’s vertices and the connection between them as its edges, protecting each node in addition to the guard nodes. This ensures that the guard nodes remain secure as well, and the network as a whole is protected.
Modular Irregular Labeling On Complete Graph And Complete Bipartite Graph R. Selvaraj, S. Vidyanandini Esic 2024 4th International Conference on Emerging Systems and Intelligent Computing Proceedings, 2024 A graph that allows for modular irregular labeling is a modular irregular labeling graph. A modular irregular labeling of a graph G of size n is a mapping of the graph’s set of edges to $1,2, \\ldots, \\mathrm{k}$ with the weights of all vertices distinct. The sum of a vertice’s incident edge labels is its weight and the weight of all vertex, determined using the method of additive modulo n. The least biggest edge label that can be used for modular irregular labeling is the modular irregularity strength. This article shows a modular irregular labeling of complete graph $K_{n}, \\mathrm{n}=3,4, \\ldots, 8$ and some families of complete bipartite graphs.
Graph Composite Labeling techniques and Practical Applications A Sethukkarasi, S Vidyanandini Esic 2024 4th International Conference on Emerging Systems and Intelligent Computing Proceedings, 2024 In this study, the intriguing concept of composite labeling within the realm of graph theory is explored. A composite labeling, represented by a bijection denoted as f, involves mapping elements from both the vertex set $V(H)$ and the edge set $E(H)$ of a graph H to integers ranging from 1 to $m+n$. A key condition imposed on this mapping is that the greatest common divisor (gcd) of $f(u v)$ and $f(v w)$ must not equal 1, where $u, v$ and w are vertices in $V(H)$. The research primarily focuses on the Star graph $k_{1, n}$ and its applications in diverse fields such as networking, blockchain, and online commerce. It is demonstrated that composite labeling is applicable to the Star graph, opening up intriguing possibilities for its use in practical scenarios. Furthermore, the exploration extends to other graph structures, including the Crown graph $\\left(C_{n} \\times K_{1}\\right)$, the Comb graph $\\left(P_{n} \\times K_{1}\\right)$, the Bistar graph $\\left(B_{n \\times n}\\right)$, the join sum of two copies of Cycle $\\left(C_{n}\\right)$, the one-point union of six copies of $P_{4}$, along with Caterpillar trees and the Flower graph $f_{(n \\times m)}$. It is established that composite labeling is a versatile concept that can be employed in various graph types. This study not only enhances the understanding of composite labeling within graph theory but also highlights its practical relevance in multiple domains. The anticipation is that these findings will inspire further research into this fascinating area, uncovering new applications and insights that can benefit both theoretical graph theory and practical network analysis.
LOCAL ANTIMAGIC LABELING OF CYCLE-RELATED GRAPHS FOR COMMUNICATION CHANNEL OPTIMIZATION IN WIRELESS SENSOR NETWORKS Dynamics of Continuous Discrete and Impulsive Systems Series B Applications and Algorithms, 2024
Even vertex odd mean labeling of some graphs R. Selvaraj, S. Vidyanandini, Soumya Ranjan Nayak Journal of Discrete Mathematical Sciences and Cryptography, 2024 This work introduces the principle of “an even point (vertex) odd ratio (mean) labeling, which is specifically applied to a graph ‘G’ consisting of ‘p’ vertices and ‘q’ edges. Even point (vertex) odd ratio (mean) labeling is exhibited by a graph G in the presence of an injectionbased function f : V of G → {0, 2, 4, ... 2q – 2, 2q} ensuring that the function derived from it (induced map) g* : E of G→{1, 3, 5, ... 2q – 1} specified by g* (uv) = g(u)+g(v)/2 is a bijection. Graphs that meet these criteria are termed an even point (vertex) odd ratio (mean) graphs. This paper explores the properties of an even point (vertex) odd ratio (mean) labeling in various graph structures.
δ and prime-labelling of a tree from caterpillars A. Sethukkarasi, S. Vidyanandini, Soumya Rajan Nayak Journal of Discrete Mathematical Sciences and Cryptography, 2024 This paper explores δ-labelling and prime labelling for trees derived from caterpillar structures. In δ-labelling, vertex labels induce injective edge labels, while prime labelling ensures adjacent vertices have a greatest common divisor of one. An algorithm for efficiently labelling caterpillar trees using both methods is introduced. These labelling techniques have practical applications in network security and cryptography, providing new strategies to strengthen the security and robustness of communication networks and cryptographic systems.
