Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

BMSA > Volume 17 > Upper Bounds for the Modified Second...
Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations
< Back to Volume

Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations

Full Text PDF

Abstract:

The modified second multiplicative Zagreb index of a connected graph G, denoted by $\prod_{2}^{*}(G)$, is defined as $\prod_{2}^{*}(G)=\prod \limits_{uv\in E(G)}[d_{G}(u)+d_{G}(v)]^{[d_{G}(u)+d_{G}(v)]}$ where $d_{G}(z)$ is the degree of a vertex z in G. In this paper, we present some upper bounds for the modified second multiplicative Zagreb index of graph operations such as union, join, Cartesian product, composition and corona product of graphs are derived.The modified second multiplicative Zagreb index of aconnected graph , denoted by , is defined as where is the degree of avertex in . In this paper, we present some upper bounds for themodified second multiplicative Zagreb index of graph operations such as union,join, Cartesian product, composition and corona product of graphs are derived.

Info:

Periodical:
Bulletin of Mathematical Sciences and Applications (Volume 17)
Pages:
10-16
DOI:
https://doi.org/10.18052/www.scipress.com/BMSA.17.10
Citation:
B. Basavanagoud and S. Patil, "Upper Bounds for the Modified Second Multiplicative Zagreb Index of Graph Operations", Bulletin of Mathematical Sciences and Applications, Vol. 17, pp. 10-16, 2016
Online since:
November 2016
Authors:
Bommanahal Basavanagoud, Shreekant Patil
Keywords:
Graph Operations, Hyper-Zagreb Index, Modified Second Multiplicative Zagreb Index, Zagreb Index
Export:
RIS, BibTeX, Text
Distribution:
Open Access

Creative Commons License
This work is licensed under a
Creative Commons Attribution 4.0 International License

References:

[1] A.R. Ashrafi, T. Doslic', A. Hamzeh, The Zagreb coindices of graph operations, Discrete Appl. Math. 158 (2010) 1571-1578.

DOI: https://doi.org/10.1016/j.dam.2010.05.017

[2] M. Azari, A. Iranmanesh, Some inequalities for the multiplicative sum Zagreb index of graph operations, J. Math. Inequal. 9(3) (2015) 727-738.

[3] B. Basavanagoud, S. Patil, A note on hyper-Zagreb index of graph operations, Iranian J. Math. Chem. 7(1) (2016) 89-92.

[4] B. Basavanagoud, S. Patil, A note on hyper-Zagreb coindex of graph operations, J. Appl. Math. Comput. (2016) 1-9.

[5] B. Basavanagoud, S. Patil, Multiplicative Zagreb indices and coindices of some derived graphs, Opuscula Math. 36(3) (2016) 287-299.

DOI: https://doi.org/10.7494/opmath.2016.36.3.287

[6] K.C. Das et al., The multiplicative Zagreb indices of graph operations, J. Inequal. Appl. (2013) 1-14.

[7] I. Gutman, N. Trinajstic', Graph theory and molecular orbitals. Total π-electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535-538.

DOI: https://doi.org/10.1016/0009-2614(72)85099-1

[8] I. Gutman, O.E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, (1986).

[9] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, (1969).

[10] M.H. Khalifeh, H. Yousefi-Azari, A.R. Ashrafi, The first and second Zagreb indices of some graph operations, Discrete Appl. Math. 157 (2009) 804-811.

DOI: https://doi.org/10.1016/j.dam.2008.06.015

[11] M.H. Khalifeh, H. Yousefi-Azari, A. R. Ashrafi, The hyper-Wiener index of graph operations, Comput. Math. Appl. 56 (2008) 1402-1407.

DOI: https://doi.org/10.1016/j.camwa.2008.03.003

[12] J. Liu, Q. Zhang, Sharp upper bounds for multiplicative Zagreb indices, MATCH Commun. Math. Comput. Chem. 68 (2012) 231-240.

[13] G.H. Shirdel, H. Rezapour, A.M. Sayadi, The hyper-Zagreb index of graph operations, Iranian J. Math. Chem. 4(2) (2013) 213-220.

[14] N. Trinajstic', Chemical Graph Theory, CRC Press, Boca Raton, FL, (1992).

Show More Hide
Cited By:
This article has no citations.