Cover Image

Radio and radial radio numbers of certain sunflower extended graphs

Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is i...

Full description

Saved in:
Bibliographic Details
Main Authors: Kaabar, Mohammed K. A., Yenoke, Kins
Format: Article
Published: Hindawi Limited 2022
Subjects:
QA Mathematics
Online Access:http://eprints.um.edu.my/43238/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.um.eprints.43238
record_format eprints
spelling my.um.eprints.432382023-10-20T02:56:25Z http://eprints.um.edu.my/43238/ Radio and radial radio numbers of certain sunflower extended graphs Kaabar, Mohammed K. A. Yenoke, Kins QA Mathematics Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is introduced. Let G=V,E be a connected graph with diameter d and radius ρ. For any integer k, 1≤k≤d, radio k−coloring of G is an assignment φ of color (positive integer) to the vertices of G such that da,b+φa−φb≥1+k, ∀a,b∈VG, where da,b is the distance between a and b in G. The biggest natural number in the range of φ is called the radio k−chromatic number of G, and it is symbolized by rckφ. The minimum number is taken over all such radio k−chromatic numbers of φ which is called the radio k−chromatic number, denoted by rckG. For k=d and k=ρ, the radio k−chromatic numbers are termed as the radio number (rnG) and radial radio number (rrG) of G, respectively. In this research work, the relationship between the radio number and radial radio number is studied for any connected graph. Then, several sunflower extended graphs are defined, and the upper bounds of the radio number and radial radio number are investigated for these graphs. Copyright © 2022 Mohammed K. A. Kaabar and Kins Yenoke. Hindawi Limited 2022-01-30 Article PeerReviewed Kaabar, Mohammed K. A. and Yenoke, Kins (2022) Radio and radial radio numbers of certain sunflower extended graphs. International Journal of Mathematics and Mathematical Sciences, 2022. ISSN 0161-1712, DOI https://doi.org/10.1155/2022/9229409 <https://doi.org/10.1155/2022/9229409>. 10.1155/2022/9229409
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
spellingShingle QA Mathematics
Kaabar, Mohammed K. A.
Yenoke, Kins
Radio and radial radio numbers of certain sunflower extended graphs
description Communication systems including AM and FM radio stations transmitting signals are capable of generating interference due to unwanted radio frequency signals. To avoid such interferences and maximize the number of channels for a predefined spectrum bandwidth, the radio-k-chromatic number problem is introduced. Let G=V,E be a connected graph with diameter d and radius ρ. For any integer k, 1≤k≤d, radio k−coloring of G is an assignment φ of color (positive integer) to the vertices of G such that da,b+φa−φb≥1+k, ∀a,b∈VG, where da,b is the distance between a and b in G. The biggest natural number in the range of φ is called the radio k−chromatic number of G, and it is symbolized by rckφ. The minimum number is taken over all such radio k−chromatic numbers of φ which is called the radio k−chromatic number, denoted by rckG. For k=d and k=ρ, the radio k−chromatic numbers are termed as the radio number (rnG) and radial radio number (rrG) of G, respectively. In this research work, the relationship between the radio number and radial radio number is studied for any connected graph. Then, several sunflower extended graphs are defined, and the upper bounds of the radio number and radial radio number are investigated for these graphs. Copyright © 2022 Mohammed K. A. Kaabar and Kins Yenoke.
format Article
author Kaabar, Mohammed K. A.
Yenoke, Kins
author_facet Kaabar, Mohammed K. A.
Yenoke, Kins
author_sort Kaabar, Mohammed K. A.
title Radio and radial radio numbers of certain sunflower extended graphs
title_short Radio and radial radio numbers of certain sunflower extended graphs
title_full Radio and radial radio numbers of certain sunflower extended graphs
title_fullStr Radio and radial radio numbers of certain sunflower extended graphs
title_full_unstemmed Radio and radial radio numbers of certain sunflower extended graphs
title_sort radio and radial radio numbers of certain sunflower extended graphs
publisher Hindawi Limited
publishDate 2022
url http://eprints.um.edu.my/43238/
_version_ 1781704674638823424
score 13.211869

Similar Items