Square difference labeling and co-secure domination in middle graph of certain graphs
G. Sarmithasg7675@srmist.edu.inDepartment of MathematicsFaculty of College of Engineering and TechnologyKattankulathurSRM Institute of Science and TechnologyChengalpattu, Tamil Nadu, 603203, IndiaView full profile → , S. Vidyanandinividyanas@srmist.edu.inDepartment of MathematicsFaculty of College of Engineering and TechnologyKattankulathurSRM Institute of Science and TechnologyChengalpattu, Tamil Nadu, 603203, IndiaView full profile → , *Soumya Ranjan NayakCorresponding authornayak.soumya17@gmail.comSchool of Computer EngineeringKIIT Deemed to be UniversityBhubaneswar, Odisha, 751024, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Published Online:
- 26 Jun 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1994
- Pages:
- 1403–1413
Abstract
Keywords
Subject Classifications
References
[1] S. Arumugam, Karam Ebadi and Martın Manrique, Co-Secure and Secure Domination in Graphs, Utilitas Mathematica, Vol. 94, pp. 167-182, (2014).
[2] Aleena Joseph, V.Sangeetha, Bounds on co-secure domination in graphs, International Journal of Mathematics Trends and Technology, Pp. 158-164, (2018).
[3] A. Behzad, M. Behzad, C.E. Praeger, On the domination number of generalized Petersen graphs, Discrete math., pp. 603-610, (2008).
[4] Chen, Operations of Interlaced Trees and Graceful Trees. Southeast Asian Bull, Pp. 337-348, (1997).
[5] C. Berge, Theory of Graphs and its Applications, Methuen, London, (1962).
[6] Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato And Michele Torielli, Domination number of Middle Graphs, Transactions on Combinatorics, Pp. 79-91, (2023).
[7] Gabor Wiener, Maho Yokota, Carol T. Zamfirescu, Spiders everywhere, Discrete Applied Mathematics, Pp. 516-522, (2021).
[8] Gallian JA, “A dynamic survey of graph labeling”, The Electronics Journal of Combinatories, (2022).
[9] J. A. Bondy and U. S. R. Murty, Graph theory with applications, (1976).
[10] Kusum, Arti Pandey, complexity results on co-secure domination in graphs, LSNS, (2023).
[11] R. Frucht, Graceful numbering of Wheels and related Graphs, Annals of the New York Academy of Sciences, Pp. 219–229, (1979).
[12] S. Sivakumar, S. Vidyanandini, E. Sreedevi, Soumya Ranjan Nayak, Akash Kumar Bhoi, Antimagic Labeling and Square Difference Labeling for Trees and Complete Bipartite Graph, Spinger, LNNS, (2022).
[13] S. Vidyanandini, N. Parvathi, Square Difference labeling for Complete Bipartite Graphs and Trees, International Journal of Pure and Applied Mathematics, Pp. 427-434, (2018).
[14] T. Hamada, and I. Yoshimura, Traversability and connectivity of the middle graph of a graph, Discrete Math, Pp. 247-256, (1976).
[15] V. Ajitha, K.L.Princy, V.Lokesha, P.S.Ranjini, On Square Difference Graphs, International J.Math. Combin, Vol. 1, Pp. 31-40,(2012).
[16] Yun Hao Zoe, Jia Jie Liu, The co-secure domination in proper interval graphs, Discrete Applied Mathematics, Vol. 311, pp. 68-71, (2022).
