Radio Number Associated with Zero Divisor Graph
Radio antennas use different frequency bands of Electromagnetic (EM) Spectrum for switching signals in the forms of radio waves. Regulatory authorities issue a unique number (unique identifying call sign) to each radio center, that must be used in all transmissions. Each radio center propagates chan...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2187 |
| _version_ | 1797545339399438336 |
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| author | Ali N. A. Koam Ali Ahmad Azeem Haider |
| author_facet | Ali N. A. Koam Ali Ahmad Azeem Haider |
| author_sort | Ali N. A. Koam |
| collection | DOAJ |
| description | Radio antennas use different frequency bands of Electromagnetic (EM) Spectrum for switching signals in the forms of radio waves. Regulatory authorities issue a unique number (unique identifying call sign) to each radio center, that must be used in all transmissions. Each radio center propagates channels to the two nearer radio centers so they must use distinctive numbers to avoid interruption. The task of effectively apportioning channels to transmitters is known as the Channel Assignment (CA) problem. CA Problem is discussed under the topic of graph coloring by mathematicians. The radio number of a graph can be used in many parts of the field communication. In this paper, we determined the radio number of zero-divisor graphs <inline-formula><math display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><msub><mi mathvariant="double-struck">Z</mi><msup><mi>p</mi><mn>2</mn></msup></msub><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><msup><mi>q</mi><mn>2</mn></msup></msub><mo>)</mo></mrow></semantics></math></inline-formula> for <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></semantics></math></inline-formula> prime numbers. |
| first_indexed | 2024-03-10T14:14:00Z |
| format | Article |
| id | doaj.art-d25f6ea80a8a4b5a883162dae3401b1c |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:14:00Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-d25f6ea80a8a4b5a883162dae3401b1c2023-11-20T23:57:15ZengMDPI AGMathematics2227-73902020-12-01812218710.3390/math8122187Radio Number Associated with Zero Divisor GraphAli N. A. Koam0Ali Ahmad1Azeem Haider2Department of Mathematics, College of Science, New Campus, Jazan University, Jazan 45142, Saudi ArabiaCollege of Computer Science and Information Technology, Jazan University, Jazan 45142, Saudi ArabiaDepartment of Mathematics, College of Science, New Campus, Jazan University, Jazan 45142, Saudi ArabiaRadio antennas use different frequency bands of Electromagnetic (EM) Spectrum for switching signals in the forms of radio waves. Regulatory authorities issue a unique number (unique identifying call sign) to each radio center, that must be used in all transmissions. Each radio center propagates channels to the two nearer radio centers so they must use distinctive numbers to avoid interruption. The task of effectively apportioning channels to transmitters is known as the Channel Assignment (CA) problem. CA Problem is discussed under the topic of graph coloring by mathematicians. The radio number of a graph can be used in many parts of the field communication. In this paper, we determined the radio number of zero-divisor graphs <inline-formula><math display="inline"><semantics><mrow><mo>Γ</mo><mo>(</mo><msub><mi mathvariant="double-struck">Z</mi><msup><mi>p</mi><mn>2</mn></msup></msub><mo>×</mo><msub><mi mathvariant="double-struck">Z</mi><msup><mi>q</mi><mn>2</mn></msup></msub><mo>)</mo></mrow></semantics></math></inline-formula> for <inline-formula><math display="inline"><semantics><mrow><mi>p</mi><mo>,</mo><mi>q</mi></mrow></semantics></math></inline-formula> prime numbers.https://www.mdpi.com/2227-7390/8/12/2187radio labelingradio numberzero divisor graph |
| spellingShingle | Ali N. A. Koam Ali Ahmad Azeem Haider Radio Number Associated with Zero Divisor Graph Mathematics radio labeling radio number zero divisor graph |
| title | Radio Number Associated with Zero Divisor Graph |
| title_full | Radio Number Associated with Zero Divisor Graph |
| title_fullStr | Radio Number Associated with Zero Divisor Graph |
| title_full_unstemmed | Radio Number Associated with Zero Divisor Graph |
| title_short | Radio Number Associated with Zero Divisor Graph |
| title_sort | radio number associated with zero divisor graph |
| topic | radio labeling radio number zero divisor graph |
| url | https://www.mdpi.com/2227-7390/8/12/2187 |
| work_keys_str_mv | AT alinakoam radionumberassociatedwithzerodivisorgraph AT aliahmad radionumberassociatedwithzerodivisorgraph AT azeemhaider radionumberassociatedwithzerodivisorgraph |