Radial radio mean labelling of Grotzsch graph and some graphs

Selvaraj, R.; Vidyanandini, S.; Nayak, Soumya Ranjan

doi:10.47974/JDMSC-1992

Open Access Research Article

Radial radio mean labelling of Grotzsch graph and some graphs

R. Selvarajsr8449@srmist.edu.inDepartment of MathematicsKattankulathurSRM Institute of Science and TechnologyChengalpattu, Tamil Nadu, 603203, IndiaView full profile → , S. Vidyanandinividyanas@srmist.edu.inDepartment of MathematicsSRM Institute of Science and Technology, KattankulathurFaculty of College of Engineering 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

pp. 1377–1387Vol. 27Issue 4June 2024DOI: 10.47974/JDMSC-1992 Crossmark XML

Published Online:: 26 Jun 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1992
Pages:: 1377–1387

Abstract

A graph G is undirected with V vertices and E edges. This study introduces radial radio mean labelling of graphs, a novel method of graph labelling. A radial radio mean labelling of the undirected graph G is a function g : V(G) → {1, 2, …, n} that satisfies the requirement g(u) + g(v)/2 between any two nodes u, v belongs to G and r(G) is the radius of G. The greatest integer in the range of a radial radio mean labelling g is the span, and it is represented by span (g). The minimal span over all G radial radio mean labelling is known as the radial radio mean number rrmn(G). The radial radio mean number of the Grotzsch graph and some graphs have been analyzed in this paper.

Keywords

Radial radio labelling Grotzsch graph Radial radio mean labelling Triangular ladder graph Eccentricity Radius Diameter

Subject Classifications

Primary 93A30Secondary 49K15

References

[1] “A. Rosa., “On Certain Valuations of the Vertices of a Graph”, in theory of Graphs, Rome, Italy (1967).
[2] Gallian, “A dynamic survey of graph labelling”, Electronic Journal of Combinatorics, 202.
[3] Hale W K, “Frequency assignment theory and applications”, IEEE Proceedings, Vol(68), pp : 1497-1514 (1980).
[4] R.K. Yeh and J.R. Griggs, “labelling graphs with a condition at distance 2”, SIAM Journal on Discrete Mathematics, Vol. 5, pp. 1586-595 (1992).
[5] S. Vidyanandini, N. Parvathi. “Graceful labelling of a Tree from Caterpillars”, Journal of Info. Opti. Sci, 35:4, 387-393 (2014).
[6] S. Vidyanandini and N. Parvathi, “Square Difference labelling for Complete Bipartite Graphs and Trees”, IJPAM, Vol.118 (10), pp. 427-434 (2018).
[7] S. Vidyanandini, N. Parvathi and S. Sivakumar “On Edge Irregularity Strength of Complete Graphs and Complete Bipartite Graphs IJPAM, Vol. 119(14), 341-344 (2018).
[8] Chartrand.G, Zhang.P, Erwin.D, and F Harary, Radio labellings of graphs, Bulletin of the Institute of Combinatorics and its Applications, Vol. 33, pp. 77-85 (2001).
[9] Soumya Ranjan, Nayak, et al. A statistical analysis of COVID-19 using Gaussian and probabilistic model, Journal of Interdisciplinary Mathematics, 24.1, pp: 19-32 (2021).
[10] Roy, Arpita, et al. Fuzzy rule based intelligent system for user authentication based on user behavior, Journal of Discrete Mathematical Sciences and Cryptography 23.2 : 409-417 (2020).
[11] S. Vimalajenifer, K M. Kathiresan. Radial radio number of graphs.
[12] S. Vidyanandini and N. Parvathi, Graceful Labeling for Graph Pn∙K2, International Journal of Scientific and Engineering Research, Volume 6, Issue 3, pp.196-19 (2015).
[13] S. Vidyanandini, N. Parvathi. Graceful Labeling of a Tree from Caterpillars, Journal of Information and Optimization Sciences, 35:4, 387-393 (2014).
[14] Vidyanandini.S and N. Parvathi, Square Difference labeling for Complete Bipartite Graphs and Trees, IJPAM, Volume.118, No.10, pp.427-434 (2018).
[15] Arputha Jose.T, and Giridharan.M. Radial radio means labelling of Mongolian tent and Diamond graphs, International Journal for Research in Applied Science and Engineering Technology 8.7 : 2078-2083 (2020).

Views: 390Downloads: 106Citations: 1