Research Article

Effect of Vertex and Edge Deletion on Total Irregularity Index

Number: 55 June 30, 2026

Effect of Vertex and Edge Deletion on Total Irregularity Index

Abstract

Cut vertices and bridges are significant graph parts that help to separate large graphs into smaller ones to ease the calculations that need to be made by means of smaller and easier steps. Recently, the effect of removing such graph parts on several topological graph indices has been calculated. Removal of a vertex means that a member is discarded from a network together with the member's connections, and removal of an edge corresponds to removing the connection between two members in the network. Thus, the reliability of a network can be increased by removing some unwanted vertices and edges from the network by using the formulas provided here for several vertex and edge types. This paper considers the effect of vertex and edge removal on the total irregularity index. It removes several different vertex and edge types from a network and calculates their effects on the total irregularity index. The method employed here can be applied to other irregularity indices and even to other graph-theoretical indices to measure the effect of vertex or edge removal on such indices.

Keywords

Total irregularity index, vertex removal, edge removal, bridge removal, pendant path removal

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APA
Yurttas Gunes, A., Özden Ayna, H., & Cangül, İ. N. (2026). Effect of Vertex and Edge Deletion on Total Irregularity Index. Journal of New Theory, 55, 1-13. https://doi.org/10.53570/jnt.1903258
AMA
1.Yurttas Gunes A, Özden Ayna H, Cangül İN. Effect of Vertex and Edge Deletion on Total Irregularity Index. JNT. 2026;(55):1-13. doi:10.53570/jnt.1903258
Chicago
Yurttas Gunes, Aysun, Hacer Özden Ayna, and İsmail Naci Cangül. 2026. “Effect of Vertex and Edge Deletion on Total Irregularity Index”. Journal of New Theory, nos. 55: 1-13. https://doi.org/10.53570/jnt.1903258.
EndNote
Yurttas Gunes A, Özden Ayna H, Cangül İN (June 1, 2026) Effect of Vertex and Edge Deletion on Total Irregularity Index. Journal of New Theory 55 1–13.
IEEE
[1]A. Yurttas Gunes, H. Özden Ayna, and İ. N. Cangül, “Effect of Vertex and Edge Deletion on Total Irregularity Index”, JNT, no. 55, pp. 1–13, June 2026, doi: 10.53570/jnt.1903258.
ISNAD
Yurttas Gunes, Aysun - Özden Ayna, Hacer - Cangül, İsmail Naci. “Effect of Vertex and Edge Deletion on Total Irregularity Index”. Journal of New Theory. 55 (June 1, 2026): 1-13. https://doi.org/10.53570/jnt.1903258.
JAMA
1.Yurttas Gunes A, Özden Ayna H, Cangül İN. Effect of Vertex and Edge Deletion on Total Irregularity Index. JNT. 2026;:1–13.
MLA
Yurttas Gunes, Aysun, et al. “Effect of Vertex and Edge Deletion on Total Irregularity Index”. Journal of New Theory, no. 55, June 2026, pp. 1-13, doi:10.53570/jnt.1903258.
Vancouver
1.Aysun Yurttas Gunes, Hacer Özden Ayna, İsmail Naci Cangül. Effect of Vertex and Edge Deletion on Total Irregularity Index. JNT. 2026 Jun. 1;(55):1-13. doi:10.53570/jnt.1903258