Abstract
Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.
References
- Gini, C. (1912), Veriabilità e Mutabilità. Cuppini, Bologna.
- Balaji, H.; Mahmoud, H. (2017) The Gini Index of Random Trees with Applications to Caterpillars, J. Appl. Prob. 54: 701-709.
- Domicolo, C.; Mahmoud, H.M. (2019) Degree Based Gini Index for Graphs, Probability in the Engineering and Informational Sciences 34 (2): 1-15.
- Wiener, A.H. (1947) Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69: 17-20.
- Hosoya, H. (1988) On some counting polynomials in chemistry, Discrete Applied Mathematics 19: 239-257.
- Konstantinova, E.V.; Diudea, M.V. (2000) The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research, Croatica Chemica Acta 73 (2): 383-403.
- Estrada, E.; Ovidiu, I.; Gutman, I; Gutierrez, A. (1998) Rodriguez, L.; Extended Wiener indices. A new set of descriptors for quantitative structure-property studies, New J. Chem, 819-822.
- Dos ̌lic ́,T. (2008) The vertex-weighted Wiener polynomials for composite graphs, Ars Mathematica Contemporanea 1: 66-80.
- Flajolet, P.; Prodinger, H. (1987) Level number sequences for trees, Discrete Mathematics 65: 149-156.
- Tangora, M.C. (1991) Level number sequences for trees and the lambda algebra, Europen J. Combinatorics 12: 433-443.
- Şahin, B.; Şener, Ü.G. (2020) Total domination type invariants of regular dendrimer. Celal Bayar University Journal of Science 16 (2): 225-228.
- Sloane, N. J. and Ploufe, S. (1995) The Encyclopedia of Integer Sequences, Academic Press, http://oeis.org.
Abstract
Level index was introduced in 2017 for rooted trees which is a component of Gini index. In the origin, Gini index is a tool for economical investigations but Balaji and Mahmoud defined the graph theoretical applications of this index for statistical analysis of graphs. Level index is an important component of Gini index. In this paper we define a new graph polynomial which is called level polynomial and calculate the level polynomial of some classes of trees. We obtain some interesting relations between the level polynomials and some integer sequences.
References
- Gini, C. (1912), Veriabilità e Mutabilità. Cuppini, Bologna.
- Balaji, H.; Mahmoud, H. (2017) The Gini Index of Random Trees with Applications to Caterpillars, J. Appl. Prob. 54: 701-709.
- Domicolo, C.; Mahmoud, H.M. (2019) Degree Based Gini Index for Graphs, Probability in the Engineering and Informational Sciences 34 (2): 1-15.
- Wiener, A.H. (1947) Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69: 17-20.
- Hosoya, H. (1988) On some counting polynomials in chemistry, Discrete Applied Mathematics 19: 239-257.
- Konstantinova, E.V.; Diudea, M.V. (2000) The Wiener Polynomial Derivatives and Other Topological Indices in Chemical Research, Croatica Chemica Acta 73 (2): 383-403.
- Estrada, E.; Ovidiu, I.; Gutman, I; Gutierrez, A. (1998) Rodriguez, L.; Extended Wiener indices. A new set of descriptors for quantitative structure-property studies, New J. Chem, 819-822.
- Dos ̌lic ́,T. (2008) The vertex-weighted Wiener polynomials for composite graphs, Ars Mathematica Contemporanea 1: 66-80.
- Flajolet, P.; Prodinger, H. (1987) Level number sequences for trees, Discrete Mathematics 65: 149-156.
- Tangora, M.C. (1991) Level number sequences for trees and the lambda algebra, Europen J. Combinatorics 12: 433-443.
- Şahin, B.; Şener, Ü.G. (2020) Total domination type invariants of regular dendrimer. Celal Bayar University Journal of Science 16 (2): 225-228.
- Sloane, N. J. and Ploufe, S. (1995) The Encyclopedia of Integer Sequences, Academic Press, http://oeis.org.
Details
| Primary Language | English |
|---|---|
| Subjects | Neural Networks |
| Journal Section | PAPERS |
| Authors | |
| Publication Date | June 6, 2024 |
| Submission Date | April 17, 2024 |
| Acceptance Date | June 5, 2024 |
| Published in Issue | Year 2024 |
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