Cacti with extremal PI Index
The vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chem...
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University of Isfahan
2016-12-01
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| Series: | Transactions on Combinatorics |
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| Online Access: | http://toc.ui.ac.ir/article_14786_f95e820e8bf0d1325600f95c8a3d7a24.pdf |
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doaj-11c0b88c330446e3abcd14000fc44fc92020-11-24T23:15:16ZengUniversity of IsfahanTransactions on Combinatorics2251-86572251-86652016-12-01541810.22108/toc.2016.1478614786Cacti with extremal PI IndexChunxiang Wang0Shaohui Wang1Bing Wei2Central China Normal UniversityUniversity of MississippiUniversity of MississippiThe vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947. A connected graph is a cactus if any two of its cycles have at most one common vertex. In this paper, we completely determine the extremal graphs with the greatest and smallest vertex PI indices mong all cacti with a fixed number of vertices. As a consequence, we obtain the sharp bounds with corresponding extremal cacti and extend a known result.http://toc.ui.ac.ir/article_14786_f95e820e8bf0d1325600f95c8a3d7a24.pdfDistanceExtremal boundsPI indexCacti |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Chunxiang Wang Shaohui Wang Bing Wei |
| spellingShingle |
Chunxiang Wang Shaohui Wang Bing Wei Cacti with extremal PI Index Transactions on Combinatorics Distance Extremal bounds PI index Cacti |
| author_facet |
Chunxiang Wang Shaohui Wang Bing Wei |
| author_sort |
Chunxiang Wang |
| title |
Cacti with extremal PI Index |
| title_short |
Cacti with extremal PI Index |
| title_full |
Cacti with extremal PI Index |
| title_fullStr |
Cacti with extremal PI Index |
| title_full_unstemmed |
Cacti with extremal PI Index |
| title_sort |
cacti with extremal pi index |
| publisher |
University of Isfahan |
| series |
Transactions on Combinatorics |
| issn |
2251-8657 2251-8665 |
| publishDate |
2016-12-01 |
| description |
The vertex PI index $PI(G) = sum_{xy in E(G)} [n_{xy}(x) + n_{xy}(y)]$ is a distance-based molecular structure descriptor, where $n_{xy}(x)$ denotes the number of vertices which are closer to the vertex $x$ than to the vertex $y$ and which has been the considerable research in computational chemistry dating back to Harold Wiener in 1947. A connected graph is a cactus if any two of its cycles have at most one common vertex. In this paper, we completely determine the extremal graphs with the greatest and smallest vertex PI indices mong all cacti with a fixed number of vertices. As a consequence, we obtain the sharp bounds with corresponding extremal cacti and extend a known result. |
| topic |
Distance Extremal bounds PI index Cacti |
| url |
http://toc.ui.ac.ir/article_14786_f95e820e8bf0d1325600f95c8a3d7a24.pdf |
| work_keys_str_mv |
AT chunxiangwang cactiwithextremalpiindex AT shaohuiwang cactiwithextremalpiindex AT bingwei cactiwithextremalpiindex |
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1725591253616164864 |