Volume 50 | Number 3 | Year 2017 | Article Id. IJMTT-V50P521 | DOI : https://doi.org/10.14445/22315373/IJMTT-V50P521
As a molecular descriptor, the first multiplicative Zagreb index Π1(G) and Narumi- Katayama index (NK) are defined as product of squares of vertex degrees and usual product of all vertex degrees of graph G respectively. In this paper, we determine upper bound of NK index of G with maximum edge connectivity k. Also we obtain Π1(G) values for two derived graphs namely Mycielski graph and thorn graph.
[1] A Iranmanesh, M.A. Hosseinzadeh and I. Gutman, On Multiplicative Zagreb indices of graphs, Iranian J.Math. Chem., vol. 279, pp. 208-218, Feb. 2012.
[2 ] B. Borovićanin and B. Furtula, On extremal Zagreb indices of trees with given dominion number, Appl. Math. Comput., vol. 279, pp. 208-218, 2016.
[3 ] B. Borovićanin and T.A. Lampert, On the maximum and minimum Zagreb indices of trees with a given number of vertices of maximum degree, MATCH Commun. Math. Comput. Chem., vol. 74, pp. 81-96, 2015.
[4] E. Estrada, L. Torres, L. Rodrguez,, and I. Gutman, An atombond connectivity index: Modelling the enthalpy of formation of alkanes, Indian J. Chem. , vol. 37A, pp. 849- 855, 1998.
[5] H. Narumi and M. Katayama, Simple topological index. A newly devised index characterizing the topological nature of structural isomers of saturated hydrocarbons, Mem. Fac. Engin. Hokkaido Univ., vol. 16, pp. 209-214, Mar. 1984.
[6] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem., vol. 50, pp. 83-92, 2004.
[7] I. Gutman, Degree-Based Topological Indices, Croat. Chem. Acta., vol. 86, pp. 351-361, April 2013.
[8] I. Gutman, B. Ruščić, N. Trinajstić, and C. F. Wilcox Jr.,Graph Theory and Molecular Orbitals. XII. Acyclic Ployenes, J. Chem. Phys., vol. 62 , pp. 3399-3405, 1975.
[9] I. Gutman, Distance in throny graph, Publications de I’Institut Mathématique (Beograd), vol. 63, pp. 31-36, 1998.
[9] K. C. Das, K. Xu and J. Nam, On Zagreb indices of graphs, Front. Math. China, vol. 10, pp. 567-582, Feb. 2015.
[10] K. C. Das, I. Gutman and B. Furtula, On atom-bond connectivity index, Chem. Phys. Lett., vol. 511, pp. 452-454, 2011.
[11] K. C. Das and I. Gutman, Some properties of the second Zagreb index, MATCH Commun. Math. Comput. Chem., vol. 52, pp. 103-112, 2004.
[12] K. L. Collins and K. Tysdal, Dependent edges in Mycielski graphs and 4-colorings of 4-skeletons, J. Graph Theory, vol. 46, pp. 285-296, April 2004.
[13] M. Randić, Characterization of Molecular Branching, J. Am. Chem. Soc., vol. 97, pp. 6609-6615, 1975.
[14] M. Randić, On characterization of molecular branching, J. Amer. Chem. Soc., vol. 97, pp. 6609-6615, 1995.
[15] N. De, Narumi-Katayama index of some derived graphs, Bulletin of the International Mathematical Virtual Institute, vol. 7, pp. 117-128, 2017.
[16] N. De, On eccentric connectivity index and polynomial of thorn graphs, Appl. Math., vol. 3, pp. 931-934, 2012.
[17] R. Todeschini and V. Consonni, A new local vertex invariants and molecular descriptors based on functions of the vertex degrees, MATCH Commun. Math. Comput. Chem., vol. 64, pp. 359-372, 2010.
[18] S. Wang, On the sharp upper and lower bounds of multiplicative Zagreb indices of graphs with connectivity at most , arXiv:174.06943v1[math. CO], 23 April, 2017.
[19] X. F. Pan, H.Q. Liu and J.M. Xu, Sharp lower bounds for the general Randi index of trees with a given size of matching, MATCH Commun. Math. Comput. Chem., vol. 54, pp. 465-480, 2005.
[20] Ž. Tomović and I. Gutman, Narumi-Katayama index of phenylenes, J. Serb. Chem. Soc., vol. 66, pp. 243-247, April 2010.
N. Konch, P. Borah, "Some new results on multiplicative topological indices," International Journal of Mathematics Trends and Technology (IJMTT), vol. 50, no. 3, pp. 134-138, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V50P521