Öz
Vertex and edge addition/deletion to a given graph is a useful method to study several required properties of a given graph or graph class. Successively applying these methods, one can obtain such information on a large graph by means of smaller graphs. In this work, we studied the effects of adding a new edge to a graph on the reduced second Zagreb index and hyper-Zagreb index.
Anahtar Kelimeler
Reduced second Zagreb index hyper-Zagreb index edge addition vertex addition
Kaynakça
- Wiener, H. J., Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69, 17-20, (1947).
- Gutman, I. ve Trinajstic, N., Graph theory and molecular orbitals III, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538, (1972).
- Das, K. C., Akgunes, N., Togan, M., Yurttas, A., Cangul, I., N. ve Cevik, A. S., On the first Zagreb index and multiplicative Zagreb coindices of graphs, Analele Stiintifice ale Universitatii Ovidius Constanta 24, 1, 153-176, (2016).
- Das, K. C. ve Gutman, I., Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., 52, 103-112, (2004).
- Gutman, I., Furtula, B. ve Elphick C., Three new/old vertex degree-based topological indices, MATCH Commun. Math. Comput. Chem., 72, 617-684, (2014).
- Furtula, B., Gutman, I. ve Ediz S., On difference of Zagreb indices, Discrete Appl. Math. 178, 83-88, (2014).
- Shirdel, G. H., Rezapour, H. ve Sayadi A. M., The hyper–Zagreb index of graph operations, Iran. J. Math. Chem., 4, 213–220, (2013).
- Delen, S. ve Cangul, I. N., Effect of edge and vertex addition on Albertson and Bell indices, AIMS Mathematics, 6, 1, 925–937, (2020).
- Delen, S., Togan, M., Yurttas, A. ve Cangul, I.N., New results on edge and vertex deletion in graphs, MICOPAM Proceedings Book, 175-179, (2018).
- Togan, M., Yurttas, A., Cevik, A. S. ve Cangul, I. N., Effect of edge deletion and addition on Zagreb indices of graphs in Taş, K., Baleanu, D. ve Machado, J., Mathematical Methods in Engineering, Theoretical Aspects, Nonlinear Systems and Complexity, Springer, 191-201, USA, (2019).
- Bondy, J. A. ve Murty, U. S. R., Graph theory with applications, Macmillan London and Elsevier, New York, (1976).
Öz
Bir grafa kenar/köşe ekleme ya da bir graftan kenar/köşe silme işlemi, verilen bir graf ya da graf sınıfının gerekli birçok özelliğini çalışmada oldukça kullanışlı bir yöntemdir. Bu yöntemi art arda uygulayarak daha küçük graftan elde edilen daha büyük bir graf hakkında bilgi edinilebilir. Bu çalışmada, bir grafa yeni bir kenar eklemenin indirgenmiş ikinci Zagreb indeks ve hyper-Zagreb indeks üzerine etkisi incelenmiştir.
Anahtar Kelimeler
İndirgenmiş ikinci Zagreb indeks hyper-Zagreb indeks kenar ekleme köşe ekleme
Kaynakça
- Wiener, H. J., Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc., 69, 17-20, (1947).
- Gutman, I. ve Trinajstic, N., Graph theory and molecular orbitals III, Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett., 17, 535-538, (1972).
- Das, K. C., Akgunes, N., Togan, M., Yurttas, A., Cangul, I., N. ve Cevik, A. S., On the first Zagreb index and multiplicative Zagreb coindices of graphs, Analele Stiintifice ale Universitatii Ovidius Constanta 24, 1, 153-176, (2016).
- Das, K. C. ve Gutman, I., Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., 52, 103-112, (2004).
- Gutman, I., Furtula, B. ve Elphick C., Three new/old vertex degree-based topological indices, MATCH Commun. Math. Comput. Chem., 72, 617-684, (2014).
- Furtula, B., Gutman, I. ve Ediz S., On difference of Zagreb indices, Discrete Appl. Math. 178, 83-88, (2014).
- Shirdel, G. H., Rezapour, H. ve Sayadi A. M., The hyper–Zagreb index of graph operations, Iran. J. Math. Chem., 4, 213–220, (2013).
- Delen, S. ve Cangul, I. N., Effect of edge and vertex addition on Albertson and Bell indices, AIMS Mathematics, 6, 1, 925–937, (2020).
- Delen, S., Togan, M., Yurttas, A. ve Cangul, I.N., New results on edge and vertex deletion in graphs, MICOPAM Proceedings Book, 175-179, (2018).
- Togan, M., Yurttas, A., Cevik, A. S. ve Cangul, I. N., Effect of edge deletion and addition on Zagreb indices of graphs in Taş, K., Baleanu, D. ve Machado, J., Mathematical Methods in Engineering, Theoretical Aspects, Nonlinear Systems and Complexity, Springer, 191-201, USA, (2019).
- Bondy, J. A. ve Murty, U. S. R., Graph theory with applications, Macmillan London and Elsevier, New York, (1976).
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Konular | Kombinatorik ve Ayrık Matematik (Fiziksel Kombinatorik Hariç) |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Erken Görünüm Tarihi | 6 Ocak 2024 |
| Yayımlanma Tarihi | 19 Ocak 2024 |
| Gönderilme Tarihi | 29 Eylül 2023 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 26 Sayı: 1 |