# New lower bounds for the second variable Zagreb index

New lower bounds for the second variable Zagreb index The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index $$M_2^{\alpha }$$ M 2 α , and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randić, the second Zagreb and the modified Zagreb indices. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Combinatorial Optimization Springer Journals

# New lower bounds for the second variable Zagreb index

, Volume 36 (1) – May 2, 2018
17 pages

/lp/springer_journal/new-lower-bounds-for-the-second-variable-zagreb-index-03qRrTQjs9
Publisher
Springer US
Subject
Mathematics; Combinatorics; Convex and Discrete Geometry; Mathematical Modeling and Industrial Mathematics; Theory of Computation; Optimization; Operations Research/Decision Theory
ISSN
1382-6905
eISSN
1573-2886
D.O.I.
10.1007/s10878-018-0293-7
Publisher site
See Article on Publisher Site

### Abstract

The aim of this paper is to obtain new sharp inequalities for a large family of topological indices, including the second variable Zagreb index $$M_2^{\alpha }$$ M 2 α , and to characterize the set of extremal graphs with respect to them. Our main results provide lower bounds on this family of topological indices involving just the minimum and the maximum degree of the graph. These inequalities are new even for the Randić, the second Zagreb and the modified Zagreb indices.

### Journal

Journal of Combinatorial OptimizationSpringer Journals

Published: May 2, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations