Vertex Switching of Some Graph Classes
Boletim da Sociedade Paranaense de Matematica, vol.44, no.9, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 9
- Publication Date: 2026
- Doi Number: 10.5269/bspm.79360
- Journal Name: Boletim da Sociedade Paranaense de Matematica
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Keywords: complete bipartite graph, complete graph, star graph, tadpole graph, vertex switched graph, Vertex switching
- Bursa Uludag University Affiliated: Yes
Abstract
Operations with several graph parts help us to reach our aimed result easier than expected. Many operations including vertex deletion, vertex addition, edge deletion, edge addition and edge contraction have been in the list of tools of graph theorists in calculating several properties of graphs. A famous example is the Birkhoff-Lewis theorem which uses edge deletion and edge contraction to calculate the chromatic polynomial of a graph recursively. Many other applications of such operations are in the hands of graph theorists and those applying graph theory to their research in other fields. Here we study a recently introduced operation called vertex switching and calculate the vertex switched graphs of some very frequently used graph classes such as complete, star, complete bipartite and tadpole graphs. Some of the obtained graphs are also known graphs, but some of the vertex switched graphs, especially of tadpole graphs, are looking like degenerate butterfly graphs.