Research Article

A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes

Number: 48 September 30, 2024
EN

A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes

Abstract

Many graph theorists have studied graph operations due to their applications and the advantages with heavy calculations. In a recent paper, the vertex-switching operation is analyzed, and some vertex-switched graphs are determined for some graph classes. This paper calculates the first Zagreb index and the second Zagreb index of vertex-switched star, complete bipartite, and tadpole graphs. It finally discusses the need for further research.

Keywords

Vertex switching, vertex switched graph, star graph, complete bipartite graph, tadpole graph

References

  1. R. Balakrishnan, K. Ranganathan, A text book of graph theory, Springer-Verlag, New York, 1999.
  2. S. Delen, I. N. Cangul, Effect of edge and vertex addition on Albertson and Bell indices, AIMS Mathematics 6 (1) (2020) 925-937.
  3. S. Delen, F. Ersoy Zihni, F. Ozen Erdogan, H. Ozden Ayna, I. N. Cangul, The effect of vertex and edge deletion on the independence number of graphs, Far East Journal of Applied Mathematics 112 (2022) 11-19.
  4. A. Yurttas Gunes, H. Ozden Ayna, I. N. Cangul, The effect of vertex and edge removal on Sombor index, Symmetry (2024) 16 170.
  5. A. Yurttas Gunes, M. Togan, F. Celik, I. N. Cangul, Cut vertex and cut edge problem for the topological indices of graphs, Journal of Taibah University for Science 13 (1) (2019) 1175-1183.
  6. S. Delen, M. Togan, A. Yurttas, U. Ana, I. N. Cangul, The effect of edge and vertex deletion on omega invariant, Applicable Analysis and Discrete Mathematics 14 (3) 2020 685-696.
  7. S. Delen, M. Togan, A. Yurttas, I. N. Cangul, New results on edge and vertex deletion in graphs, in Yılmaz Şimşek (Ed.), The Mediterranean International Conference of Pure & Applied Mathematics and Related Areas, Antalya, 2018, pp. 175-179.
  8. A. Yurttas, M. Togan, I. N. Cangul, Zagreb indices of graphs with added edges, Proceedings of the Jangjeon Mathematical Society 21 (3) (2018) 385-392.
  9. I. H. Agustin, A. S. Maragadam, D. Dafik, V. Lokesha, M. Manjunath, Semi-total point graph of neighbourhood edge corona graph of G and H, European Journal of Pure and Applied Mathematics 16 (2) (2023) 1094-1109.
  10. V. Lokesha, S. Jain, M. Manjunath, Some adriaticindices of Dutch windmill graph using graph operator, Advances and Applications in Discrete Mathematics 22 (2) (2019) 127-137.
APA
Özden Ayna, H. (2024). A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes. Journal of New Theory, 48, 48-60. https://doi.org/10.53570/jnt.1522803
AMA
1.Özden Ayna H. A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes. JNT. 2024;(48):48-60. doi:10.53570/jnt.1522803
Chicago
Özden Ayna, Hacer. 2024. “A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes”. Journal of New Theory, nos. 48: 48-60. https://doi.org/10.53570/jnt.1522803.
EndNote
Özden Ayna H (September 1, 2024) A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes. Journal of New Theory 48 48–60.
IEEE
[1]H. Özden Ayna, “A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes”, JNT, no. 48, pp. 48–60, Sept. 2024, doi: 10.53570/jnt.1522803.
ISNAD
Özden Ayna, Hacer. “A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes”. Journal of New Theory. 48 (September 1, 2024): 48-60. https://doi.org/10.53570/jnt.1522803.
JAMA
1.Özden Ayna H. A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes. JNT. 2024;:48–60.
MLA
Özden Ayna, Hacer. “A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes”. Journal of New Theory, no. 48, Sept. 2024, pp. 48-60, doi:10.53570/jnt.1522803.
Vancouver
1.Hacer Özden Ayna. A Study on Zagreb Indices of Vertex-Switching for Special Graph Classes. JNT. 2024 Sep. 1;(48):48-60. doi:10.53570/jnt.1522803