The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs
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| Title: | The Super-Connectivity of the Double Vertex Graph of Complete Bipartite Graphs |
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| Authors: | Gülnaz BORUZANLI EKİNCİ |
| Source: | Volume: 4, Issue: 4 251-257 Fundamental Journal of Mathematics and Applications |
| Publisher Information: | Fundamental Journal of Mathematics and Applications, 2021. |
| Publication Year: | 2021 |
| Subject Terms: | Matematik, Connectivity, Super connectivity, Double vertex graph, 0102 computer and information sciences, Token graph, 01 natural sciences, Mathematical Sciences |
| Description: | Let $ G=(V,E) $ be a graph. The double vertex graph $F_2(G)$ of $ G $ is the graph whose vertex set consists of all $ 2 $-subsets of $ V(G) $ such that two vertices are adjacent in $ F_2(G) $ if their symmetric difference is a pair of adjacent vertices in $ G $. The super--connectivity of a connected graph is the minimum number of vertices whose removal results in a disconnected graph without an isolated vertex. In this paper, we determine the super--connectivity of the double vertex graph of the complete bipartite graph $ K_{m,n} $ for $ m\geq 4 $ where $ n\geq m+2 $. |
| Document Type: | Article Other literature type |
| File Description: | application/pdf |
| ISSN: | 2645-8845 |
| DOI: | 10.33401/fujma.975352 |
| Access URL: | https://dergipark.org.tr/en/download/article-file/1895357 https://hdl.handle.net/11454/80900 https://doi.org/10.33401/fujma.975352 https://search.trdizin.gov.tr/yayin/detay/506754 https://dergipark.org.tr/tr/pub/fujma/issue/65925/975352 |
| Rights: | CC BY NC |
| Accession Number: | edsair.doi.dedup.....78fabc87daa2c0eacb0d65ad13d61a49 |
| Database: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstract: | Let $ G=(V,E) $ be a graph. The double vertex graph $F_2(G)$ of $ G $ is the graph whose vertex set consists of all $ 2 $-subsets of $ V(G) $ such that two vertices are adjacent in $ F_2(G) $ if their symmetric difference is a pair of adjacent vertices in $ G $. The super--connectivity of a connected graph is the minimum number of vertices whose removal results in a disconnected graph without an isolated vertex. In this paper, we determine the super--connectivity of the double vertex graph of the complete bipartite graph $ K_{m,n} $ for $ m\geq 4 $ where $ n\geq m+2 $. |
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| ISSN: | 26458845 |
| DOI: | 10.33401/fujma.975352 |