Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs
A finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3,…,k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of edges, are distinct. In this paper, we show t...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/3203108 |
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| _version_ | 1832549048653971456 |
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| author | Sumiya Nasir Nazeran Idrees Afshan Sadiq Fozia Bashir Farooq Salma Kanwal Muhammad Imran |
| author_facet | Sumiya Nasir Nazeran Idrees Afshan Sadiq Fozia Bashir Farooq Salma Kanwal Muhammad Imran |
| author_sort | Sumiya Nasir |
| collection | DOAJ |
| description | A finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3,…,k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of edges, are distinct. In this paper, we show that the diamond graph Brn for 𝑛 ≥ 3, umbrella graph Um,n, and generalized Petersen graph GPn,k, for n≥3 and 1≤k<n/2, admit strongly multiplicative labeling. Moreover, strongly multiplicative labeling of a double comb graph and sunflower planar graph has also been investigated and elaborated as well with different examples. |
| format | Article |
| id | doaj-art-94bc8960085a4144bbcbd12bcc37a3cf |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-94bc8960085a4144bbcbd12bcc37a3cf2025-02-03T06:12:24ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/3203108Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other GraphsSumiya Nasir0Nazeran Idrees1Afshan Sadiq2Fozia Bashir Farooq3Salma Kanwal4Muhammad Imran5College of Science and Human StudiesDepartment of MathematicsAbdus Salam School of Mathematical SciencesDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsA finite, simple graph of order k is said to be a strongly multiplicative graph when all vertices of the graph are labeled by positive integers 1,2,3,…,k such that the induced edge labels of the graph, obtained by the product of labels of end vertices of edges, are distinct. In this paper, we show that the diamond graph Brn for 𝑛 ≥ 3, umbrella graph Um,n, and generalized Petersen graph GPn,k, for n≥3 and 1≤k<n/2, admit strongly multiplicative labeling. Moreover, strongly multiplicative labeling of a double comb graph and sunflower planar graph has also been investigated and elaborated as well with different examples.http://dx.doi.org/10.1155/2022/3203108 |
| spellingShingle | Sumiya Nasir Nazeran Idrees Afshan Sadiq Fozia Bashir Farooq Salma Kanwal Muhammad Imran Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs Journal of Mathematics |
| title | Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs |
| title_full | Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs |
| title_fullStr | Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs |
| title_full_unstemmed | Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs |
| title_short | Strongly Multiplicative Labeling of Diamond Graph, Generalized Petersen Graph, and Some Other Graphs |
| title_sort | strongly multiplicative labeling of diamond graph generalized petersen graph and some other graphs |
| url | http://dx.doi.org/10.1155/2022/3203108 |
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