A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index
In 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range of applications. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubs...
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MDPI AG
2022-12-01
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| author | Guifu Su Guanbang Song Junfeng Du Weixing Yang Gang Rao Jun Yin |
| author_facet | Guifu Su Guanbang Song Junfeng Du Weixing Yang Gang Rao Jun Yin |
| author_sort | Guifu Su |
| collection | DOAJ |
| description | In 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range of applications. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> be the class of bipartite graphs of order <i>n</i> and diameter <i>d</i>. In this paper, we mainly characterize the bipartite graphs in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> with the maximal inverse sum indeg index. Bipartite graphs with the largest, second-largest, and smallest inverse sum indeg indexes are also completely characterized. |
| first_indexed | 2024-03-09T17:20:16Z |
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| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T17:20:16Z |
| publishDate | 2022-12-01 |
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| spelling | doaj.art-90698b1bbe794a908ee9873ffa2f12762023-11-24T13:15:31ZengMDPI AGAxioms2075-16802022-12-01111269110.3390/axioms11120691A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg IndexGuifu Su0Guanbang Song1Junfeng Du2Weixing Yang3Gang Rao4Jun Yin5College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, ChinaCollege of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, ChinaCollege of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, ChinaCollege of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, ChinaCollege of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, ChinaSchool of Computer, Qinghai Normal University, Xining 810000, ChinaIn 2010, Vukičević introduced an new graph invariant, the inverse sum indeg index of a graph, which has been studied due to its wide range of applications. Let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> be the class of bipartite graphs of order <i>n</i> and diameter <i>d</i>. In this paper, we mainly characterize the bipartite graphs in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi mathvariant="script">B</mi><mrow><mi>n</mi></mrow><mi>d</mi></msubsup></semantics></math></inline-formula> with the maximal inverse sum indeg index. Bipartite graphs with the largest, second-largest, and smallest inverse sum indeg indexes are also completely characterized.https://www.mdpi.com/2075-1680/11/12/691the inverse sum indeg indexbipartite graphsdiameterextremal graphs |
| spellingShingle | Guifu Su Guanbang Song Junfeng Du Weixing Yang Gang Rao Jun Yin A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index Axioms the inverse sum indeg index bipartite graphs diameter extremal graphs |
| title | A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index |
| title_full | A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index |
| title_fullStr | A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index |
| title_full_unstemmed | A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index |
| title_short | A Complete Characterization of Bipartite Graphs with Given Diameter in Terms of the Inverse Sum Indeg Index |
| title_sort | complete characterization of bipartite graphs with given diameter in terms of the inverse sum indeg index |
| topic | the inverse sum indeg index bipartite graphs diameter extremal graphs |
| url | https://www.mdpi.com/2075-1680/11/12/691 |
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