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...

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Main Authors: Mohammed K. A. Kaabar, Kins Yenoke
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2022/9229409
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author Mohammed K. A. Kaabar
Kins Yenoke
author_facet Mohammed K. A. Kaabar
Kins Yenoke
author_sort Mohammed K. A. Kaabar
collection DOAJ
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.
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publishDate 2022-01-01
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series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-3d30f57cb4394a459e9d1f73483011c52025-02-03T00:59:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/9229409Radio and Radial Radio Numbers of Certain Sunflower Extended GraphsMohammed K. A. Kaabar0Kins Yenoke1Gofa CampDepartment of MathematicsCommunication 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.http://dx.doi.org/10.1155/2022/9229409
spellingShingle Mohammed K. A. Kaabar
Kins Yenoke
Radio and Radial Radio Numbers of Certain Sunflower Extended Graphs
International Journal of Mathematics and Mathematical Sciences
title 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_short Radio and Radial Radio Numbers of Certain Sunflower Extended Graphs
title_sort radio and radial radio numbers of certain sunflower extended graphs
url http://dx.doi.org/10.1155/2022/9229409
work_keys_str_mv AT mohammedkakaabar radioandradialradionumbersofcertainsunflowerextendedgraphs
AT kinsyenoke radioandradialradionumbersofcertainsunflowerextendedgraphs