Cactus Graphs with Maximal Multiplicative Sum Zagreb Index
A connected graph <i>G</i> is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of a graph <i>G</i> is the product of the sum of the degrees of adjacent vertices in <i>G</i>. In this paper, we introduce se...
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/913 |
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| author | Chunlei Xu Batmend Horoldagva Lkhagva Buyantogtokh |
| author_facet | Chunlei Xu Batmend Horoldagva Lkhagva Buyantogtokh |
| author_sort | Chunlei Xu |
| collection | DOAJ |
| description | A connected graph <i>G</i> is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of a graph <i>G</i> is the product of the sum of the degrees of adjacent vertices in <i>G</i>. In this paper, we introduce several graph transformations that are useful tools for the study of the extremal properties of the multiplicative sum Zagreb index. Using these transformations and symmetric structural representations of some cactus graphs, we determine the graphs having maximal multiplicative sum Zagreb index for cactus graphs with the prescribed number of pendant vertices (cut edges). Furthermore, the graphs with maximal multiplicative sum Zagreb index are characterized among all cactus graphs of the given order. |
| first_indexed | 2024-03-10T11:13:24Z |
| format | Article |
| id | doaj.art-95412a0e812a482a9ef816fdf77c862a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:13:24Z |
| publishDate | 2021-05-01 |
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| series | Symmetry |
| spelling | doaj.art-95412a0e812a482a9ef816fdf77c862a2023-11-21T20:37:27ZengMDPI AGSymmetry2073-89942021-05-0113591310.3390/sym13050913Cactus Graphs with Maximal Multiplicative Sum Zagreb IndexChunlei Xu0Batmend Horoldagva1Lkhagva Buyantogtokh2Department of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar 210648, MongoliaDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar 210648, MongoliaDepartment of Mathematics, Mongolian National University of Education, Baga toiruu-14, Ulaanbaatar 210648, MongoliaA connected graph <i>G</i> is said to be a cactus if any two cycles have at most one vertex in common. The multiplicative sum Zagreb index of a graph <i>G</i> is the product of the sum of the degrees of adjacent vertices in <i>G</i>. In this paper, we introduce several graph transformations that are useful tools for the study of the extremal properties of the multiplicative sum Zagreb index. Using these transformations and symmetric structural representations of some cactus graphs, we determine the graphs having maximal multiplicative sum Zagreb index for cactus graphs with the prescribed number of pendant vertices (cut edges). Furthermore, the graphs with maximal multiplicative sum Zagreb index are characterized among all cactus graphs of the given order.https://www.mdpi.com/2073-8994/13/5/913multiplicative sum Zagreb indexcactus graphpendant vertexcut edge |
| spellingShingle | Chunlei Xu Batmend Horoldagva Lkhagva Buyantogtokh Cactus Graphs with Maximal Multiplicative Sum Zagreb Index Symmetry multiplicative sum Zagreb index cactus graph pendant vertex cut edge |
| title | Cactus Graphs with Maximal Multiplicative Sum Zagreb Index |
| title_full | Cactus Graphs with Maximal Multiplicative Sum Zagreb Index |
| title_fullStr | Cactus Graphs with Maximal Multiplicative Sum Zagreb Index |
| title_full_unstemmed | Cactus Graphs with Maximal Multiplicative Sum Zagreb Index |
| title_short | Cactus Graphs with Maximal Multiplicative Sum Zagreb Index |
| title_sort | cactus graphs with maximal multiplicative sum zagreb index |
| topic | multiplicative sum Zagreb index cactus graph pendant vertex cut edge |
| url | https://www.mdpi.com/2073-8994/13/5/913 |
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