Prime Labeling of Special Graphs

• Author(s): M. D. M. C. P. Weerarathna; T. R. D. S. M. Thennakoon; A. C. G. Perera
• Paper ID: 1702358
• Page: 84-86
• Published Date: 12-06-2020
• Published In: Iconic Research And Engineering Journals
• Publisher: IRE Journals
• e-ISSN: 2456-8880
• Volume/Issue: Volume 3 Issue 12 June-2020

Abstract

In this paper we investigate the prime labeling of newly constructed graphs. The symbols V(G) and E(G) will denote the vertex set and edge set of a graph G. A graph G=(V(G),E(G) )with |V(G)| vertices is said to have prime labeling if there exist a bijection mapf?V(G) ? {1,2,3,?,|V(G)|} such that for each edge e=uv in E(G),f(u) and f (v) are relatively prime. Two integers are said to be relatively prime, if their greatest common divisor(gcd) is 1. We proved that the graphs obtained by replacing every edge of a star graph K1,n by C_m is a prime graph, where n ? 1 and m?4.

Keywords

Prime labeling, Prime graphs, Greatest common divisor, Star Graphs, Cyclic Graphs

Citations

IRE Journals:
M. D. M. C. P. Weerarathna, T. R. D. S. M. Thennakoon, A. C. G. Perera "Prime Labeling of Special Graphs" Iconic Research And Engineering Journals Volume 3 Issue 12 2020 Page 84-86

IEEE:
M. D. M. C. P. Weerarathna, T. R. D. S. M. Thennakoon, A. C. G. Perera "Prime Labeling of Special Graphs" Iconic Research And Engineering Journals, vol. 3, no. 12, Jun. 2020

APA:
M. D. M. C. P. Weerarathna, T. R. D. S. M. Thennakoon, A. C. G. Perera (2020). Prime Labeling of Special Graphs. Iconic Research And Engineering Journals, 3(12).

MLA:
M. D. M. C. P. Weerarathna, T. R. D. S. M. Thennakoon, A. C. G. Perera "Prime Labeling of Special Graphs" Iconic Research And Engineering Journals, vol. 3, no. 12, Jun. 2020.

BibTeX

@article{1702358,
author = {M. D. M. C. P. Weerarathna, T. R. D. S. M. Thennakoon, A. C. G. Perera},
title = {Prime Labeling of Special Graphs},
journal = {Iconic Research And Engineering Journals},
year = {2020},
volume = {3},
number = {12},
pages = {84-86},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1702358.pdf},
abstract = {In this paper we investigate the prime labeling of newly constructed graphs. The symbols V(G) and E(G) will denote the vertex set and edge set of a graph G. A graph G=(V(G),E(G) )with |V(G)| vertices is said to have prime labeling if there exist a bijection mapf?V(G) ? {1,2,3,?,|V(G)|} such that for each edge e=uv in E(G),f(u) and f (v) are relatively prime. Two integers are said to be relatively prime, if their greatest common divisor(gcd) is 1. We proved that the graphs obtained by replacing every edge of a star graph K1,n by C_m is a prime graph, where n ? 1 and m?4.},
keywords = {Prime labeling, Prime graphs, Greatest common divisor, Star Graphs, Cyclic Graphs},
month = {June}
}