Irregularity Sombor index. (English) Zbl 1532.05043
Summary: The irregularity Sombor index ISO is a recently introduced measure for graph irregularity, defined as the sum over all pairs of adjacent vertices \(u,v\) of the term \(\sqrt{|d_u^2 -d_v^2|}\), where \(d_u\) is the degree of the vertex \(u\). Some basic mathematical properties of ISO are established.
MSC:
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
| 05C07 | Vertex degrees |
| 05C92 | Chemical graph theory |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
Keywords:
degree of vertex; irregularity of graph; irregularity measure; irregularity index; Sombor indexReferences:
| [1] | H. Abdo, D. Dimitrov, I. Gutman, Graph irregularity and its measures, Appl. Math. Comput. 357 (2019), 317-324. · Zbl 1428.05300 |
| [2] | M. O. Albertson, The irregularity of a graph, Ars Comb. 46 (1997), 219-225. · Zbl 0933.05073 |
| [3] | A. Ali, G. Chartrand, P. Zhang, Irregularity in Graphs, Springer, Cham, 2021. · Zbl 1472.05001 |
| [4] | A. R. Ashrafi, A. Ghalavand, Note on non-regular graphs with minimal total irregu-larity, Appl. Math. Comput. 369 (2020), #124891. · Zbl 1433.05079 |
| [5] | L. Buyantogtokh, E. Azjargal B. Horoldagva, S. Dorjsembe, D. Adiyanyam, On the maximum size of stepwise irregular graphs, Appl. Math. Comput. 392 (2021), #125683. · Zbl 1508.05025 |
| [6] | S. Dorjsembe, L. Buyantogtokh, I. Gutman, B. Horoldagva, T. Réti, Irregularity of graphs, MATCH Commun. Math. Comput. Chem. 89 (2023), 371-388. · Zbl 1505.92277 |
| [7] | G. H. Fath-Tabar, I. Gutman, R. Nasiri, Extremely irregular trees, Bull. Acad. Serbe Sci. Arts (Cl. Math.) 153 145 (2013), 1-8. · Zbl 1299.05053 |
| [8] | A. Ghalavand, I. Gutman, M. Tavakoli, Irregularity measure of graphs, J. Math., in press. |
| [9] | A. Ghalavand, T. Sohail, On some variations of the irregularity, Discrete Math. Lett. 3 (2020), 25-30. · Zbl 1463.05053 |
| [10] | I. Gutman, Geometric approach to degree-based topological indices: Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021), 11-16. · Zbl 1474.92154 |
| [11] | I. Gutman, Sombor index -one year later, Bull. Acad. Serbe Sci. Arts (Cl. Math.) 153 (2020), 43-55. · Zbl 1476.05033 |
| [12] | I. Gutman, T. Réti, Note on irregular graphs, Bull. Acad. Serbe Sci. Arts (Cl. Math.) 151 (2018), 5-16. · Zbl 1467.05036 |
| [13] | K. Hamid, M. W. Iqbal, Q. Abbas, M. Arif, A. Brezulianu, O. Geman, Discovering irregularities from computer networks by topological mapping, Appl. Sci. 12 (2022), #12051. |
| [14] | K. Hamid, M. W. Iqbal, S. U. Bhatti, N. Hussain, M. Fatima, S. Ramzan, Irregularity investigation of certain computer networks empowered security, J. Jilin Univ. 41(12) (2022), 75-93. |
| [15] | V. R. Kulli, New irregularity Sombor indices and new adriatic (a, b)-KA indices of certain chemical drugs, Int. J. Math. Trends Technol. 67(9) (2021), 105-113. |
| [16] | Z. Lin, T. Zhou, X.Wang, L. Miao, The general Albertson irregularity index of graphs, AIMS Math. 7 (2022), 25-38. Faculty of Science University of Kragujevac P. O. Box 60 34000 Kragujevac Serbia e-mail: gutman@kg.ac.rs Department of Mathematics Gulbarga University Kalaburgi 585 106 |
| [17] | India e-mail: vrkulli@gmail.com State University of Novi Pazar Novi Pazar Serbia e-mail: iredzepovic@np.ac.rs |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
