The multiplicative Zagreb indices of graph operations

Springer Science and Business Media LLC - 2013
Kinkar Ch. Das1, Aysun Yurttaş2, Müge Togan2, A. Sinan Çevik3, İsmaıl Nacı Cangül2
1Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea
2Department of Mathematics, Faculty of Arts and Science, Uludağ University, Gorukle Campus, Bursa, 16059, Turkey
3Department of Mathematics, Faculty of Science, Selçuk University, Campus, Konya, 42075, Turkey

Tóm tắt

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:

∏ 1 = ∏ 1 ( G ) = ∏ v ∈ V ( G ) d G ( v ) 2 , ∏ 2 = ∏ 2 ( G ) = ∏ u v ∈ 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.

Từ khóa


Tài liệu tham khảo

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Todeschini R, Consonni V: New local vertex invariants and molecular descriptors based on functions of the vertex degrees. MATCH Commun. Math. Comput. Chem. 2010, 64: 359–372.

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