The multiplicative Zagreb indices of graph operations
Date
2013
Authors
Das, Kinkar C.
Çevik, Ahmet Sinan
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
Recently, Todeschini et al. (Novel Molecular Structure Descriptors - Theory and Applications I, pp. 73-100, 2010), Todeschini and Consonni (MATCH Commun. Math. Comput. Chem. 64:359-372, 2010) have proposed the multiplicative variants of ordinary Zagreb indices, which are defined as follows:
Pi(1) = Pi(1)(G) = Pi(v is an element of V(G)) d(G)(V)(2), Pi(2) = Pi(2)(G) = Pi(uv is an element of E(G)) d(G)(u)d(G)(V).
These two graph invariants are called multiplicative Zagreb indices by Gutman (Bull. Soc. Math. Banja Luka 18:17-23, 2011). In this paper the upper bounds on the multiplicative Zagreb indices of the join, Cartesian product, corona product, composition and disjunction of graphs are derived and the indices are evaluated for some well-known graphs.
MSC: 05C05, 05C90, 05C07.
Description
Keywords
Mathematics, Graph, Multiplicative Zagreb index, Graph operations, Trees, 1st
Citation
Das, K. C. vd. (2013). "The multiplicative Zagreb indices of graph operations". Journal of Inequalities and Applications, 2013(90), 1-14.