Affiliation:
1. Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, Bursa 16059, Turkey
Abstract
A vertex degree based topological index called the Sombor index was recently defined in 2021 by Gutman and has been very popular amongst chemists and mathematicians. We determine the amount of change of the Sombor index when some elements are removed from a graph. This is done for several graph elements, including a vertex, an edge, a cut vertex, a pendant edge, a pendant path, and a bridge in a simple graph. Also, pendant and non-pendant cases are studied. Using the obtained formulae successively, one can find the Sombor index of a large graph by means of the Sombor indices of smaller graphs that are just graphs obtained after removal of some vertices or edges. Sometimes, using iteration, one can manage to obtain a property of a really large graph in terms of the same property of many other subgraphs. Here, the calculations are made for a pendant and non-pendant vertex, a pendant and non-pendant edge, a pendant path, a bridge, a bridge path from a simple graph, and, finally, for a loop and a multiple edge from a non-simple graph. Using these results, the Sombor index of cyclic graphs and tadpole graphs are obtained. Finally, some Nordhaus–Gaddum type results are obtained for the Sombor index.
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference27 articles.
1. Sombor indices-back to geometry;Gutman;Open J. Discret. Appl. Math.,2022
2. Some basic properties of Sombor indices;Gutman;Open J. Discret. Appl. Math.,2021
3. Geometric approach to degree-based topological indices: Sombor indices;Gutman;MATCH Commun. Math. Comput. Chem.,2021
4. Molecular trees with extremal values of Sombor indices;Deng;Int. J. Quantum Chem.,2021
5. Block Sombor index of a graph and its matrix representation;Devaragudi;Open J. Discret. Appl. Math.,2023