Reduced second Zagreb index of product graphs
https://doi.org/10.17586/2220-8054-2020-11-2-131-137
Аннотация
The reduced second Zagreb index of a graph G is defined as RM2(G) = X (dG(u)−1)(dG(v)−1), where dG(v) denotes the degree uv∈E(G) of the vertex v of graph G. Recently Furtula et al. (Furtula B., Gutman I., Ediz S. Discrete Appl. Math., 2014) characterized the maximum trees with respect to reduced second Zagreb index. The aim of this paper is to compute reduced second Zagreb index of the Cartesian product of k (≥ 2) number of graphs and hence as a consequence the reduced second Zagreb index of some special graphs applicable in various real world problems are computed. Topological properties of different nanomaterials like nanotube, nanotorus etc. are studied here graphically in terms of the aforesaid aforementioned index.
Об авторе
N. De
Department of Basic Sciences and Humanities (Mathematics),
Calcutta Institute of Engineering and Management
Индия
Индия
Список литературы
1. Trinajstic N.´ Chemical Graph Theory. CRC Press, Boca Raton, 1993.
2. Gutman I., Polansky O.E. Mathematical Concepts in Organic Chemistry. Springer, Berlin, 1986.
3. Wiener H. Structural determination of paraffin boiling points. J. Am. Chem. Soc., 1947, 69, P. 7–20.
4. Randic M. Quantitative Structure – Property Relationship: boiling points and planar benzenoids.´ New. J. Chem., 1996, 20(10), P. 1001–1009.
5. Hawkins D.M., Basak S.C., Mills D. Assessing Model Fit by Cross Validation. J. Chem. Inf. Comput. Sci., 2003, 43, P. 579–586.
6. Gutman I, Trinajstic N. Graph theory and molecular orbitals. Total´ π-electron energy of alternate hydrocarbons. Chem. Phys. Lett., 1972, 17, P. 535–538.
7. Gutman I, Ruci´ c B, Trinajsti´ c N, Wilcox C.F. Graph theory and molecular orbitals. XII. Acyclic polyenes.´ J. Chem. Phys., 1975, 62, P. 3399– 3405.
8. Das K.C., Xu K., Gutman I. On Zagreb and Harary indices. MATCH Commun. Math. Comput Chem., 2013, 70, P. 301–314.
9. Azari M., Iranmanesh A., Gutman I. Zagreb indices of bridge and chain graphs. MATCH Commun. Math. Comput. Chem., 2013, 70, P. 921– 938.
10. Hamzeh A., Reti T. An analogue of Zagreb index inequality obtained from graph ir-regularity measures. MATCH Commun. Math. Comput. Chem., 2014, 72, P. 669–683.
11. Li S., Zhang M.J. Sharp upper bounds for the Zagreb indices of bipartite graphs with a given diameter. Appl. Math. Lett., 2011, 24, P. 131–137.
12. Fonseca C.M.D., Stevanovic D. Further properties of the second Zagreb index. MATCH Commun. Math. Comput. Chem., 2014, 72, P. 655–668.
13. Gutman I., Das K.C. The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem., 2004, 50, P. 83–92.
14. Mondal S., Bhosale A., De N., Pal A. Topological properties of some nanostructures. Nanosystems: Physics, Chemistry, Mathematics, 2020, 11 (1), P. 14–24.
15. Furtula B., Gutman I., Ediz S. On difference of Zagreb indices. Discrete Appl. Math., 2014, 178, P. 83–88.
16. Horoldagva H., Buyantogtokh L., Dorjsembe S. Difference of Zagreb indices andreduced second Zagreb index of cyclic graphs with cut edges. MATCH Commun. Math.Comput. Chem., 2017, 78, P. 337–349.
17. Mahanta A., Buragohain J., Bharali A. Reduced first Zagreb index, Reduced second Zagreb index and hyper-Zagreb index of four new sums based on tensor product of graphs. Global journal of engineering science and researches, 2018, 5 (11), P. 12–19.
18. Khalifeh M.H., Azari H.Y, Ashrafi A.R. The first and second Zagreb indices of some graph operations. Discrete Appl. Math., 2009, 157, P. 804–811.
19. Azari H.Y, Manoochehrian B, Ashrafi A.R. The PI index of product graphs. Appl. Math. Lett., 2008, 21, P. 624–627.
20. Klavzar S., Rajapakse A., Gutman I. The Szeged and the Wiener index of graphs. Appl. Math. Lett., 1996, 9, P. 45–49.
21. Graovac A., Pisanski T. On the Wiener index of a graph. J. Math. Chem., 1991, 8, P. 53–62.
22. De N., Nayeem S.M.A., Pal A. F-Index of some graph operations. 2016, Discrete Math. Algorithm Appl., 8, Article ID: 1650025.
23. De N., Nayeem S.M.A., Pal A. The F-coindex of some graph operations. 2016, Springer Plus, 5, P. 221–233.
24. De N., Nayeem S.M.A., Pal A. Reformulated First Zagreb Index of Some Graph Operations. Mathematics, 2015, 3(4), P. 945–960.
25. De N., Pal A., Nayeem S.M.A. On some bounds and exact formulae for connective eccentric indices of graphs under some graph operations. Int. J. Comb., 2014, 2014, Article ID 579257.
Рецензия
Для цитирования:
. Наносистемы: физика, химия, математика. 2020;11(2):131–137. https://doi.org/10.17586/2220-8054-2020-11-2-131-137
For citation:
De N. Reduced second Zagreb index of product graphs. Nanosystems: Physics, Chemistry, Mathematics. 2020;11(2):131–137. https://doi.org/10.17586/2220-8054-2020-11-2-131-137
Просмотров:
7
Послать статью по эл. почте 