International Journal of Combinatorics
Volume 2012 (2012), Article ID 909285, 10 pages
http://dx.doi.org/10.1155/2012/909285
Research Article

The 𝑎 and ( 𝑎 , 𝑏 ) -Analogs of Zagreb Indices and Coindices of Graphs

Toufik Mansour1 and Chunwei Song2

1Department of Mathematics, University of Haifa, 31905 Haifa, Israel
2School of Mathematical Sciences, LMAM, Peking University, Beijing 100871, China

Received 9 September 2011; Accepted 20 October 2011

Academic Editor: Alois Panholzer

Copyright © 2012 Toufik Mansour and Chunwei Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The first and second Zagreb indices were first introduced by Gutman and Trinajstić (1972). It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical instances, and in elsewhere. Recently, the first and second Zagreb coindices, a new pair of invariants, were introduced in Došlić (2008). In this paper we introduce the 𝑎 and ( 𝑎 , 𝑏 )-analogs of the above Zagreb indices and coindices and investigate the relationship between the enhanced versions to get a unified theory.