Sharp bounds for Zagreb indices of maximal outerplanar graphs

Authors:
Ailin Hou;Shuchao Li;Lanzhen Song;Bing Wei
Affiliations:
Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China 430079;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, People's Republic of China 430079;Department of Mathematics, University of Mississippi University, Oxford, USA 38677;Department of Mathematics, University of Mississippi University, Oxford, USA 38677
Venue:
Journal of Combinatorial Optimization
Year:
2011

Citing 9
Cited 2

Maximal outerplanar graphs with perfect face-independent vertex covers

Discrete Applied Mathematics - Special issue: efficient algorithms and partial k-trees
An upper bound on the sum of squares of degrees in a graph

Discrete Mathematics
Extremal graphs for weights

Discrete Mathematics
Linear Algorithms for Isomorphism of Maximal Outerplanar Graphs

Journal of the ACM (JACM)
L(h,1)-labeling subclasses of planar graphs

Journal of Parallel and Distributed Computing
(n,e)-Graphs with maximum sum of squares of degrees*

Journal of Graph Theory
Minimizer graphs for a class of extremal problems

Journal of Graph Theory
Randić ordering of chemical trees

Discrete Applied Mathematics
Trees of extremal connectivity index

Discrete Applied Mathematics

Sharp bounds for the Zagreb indices of bicyclic graphs with k-pendant vertices

Discrete Applied Mathematics
Sharp bounds of the Zagreb indices of k-trees

Journal of Combinatorial Optimization

Quantified Score

Hi-index	0.00

Visualization

Abstract

For a (molecular) graph, the first Zagreb index M 1 is equal to the sum of squares of the vertex degrees, and the second Zagreb index M 2 is equal to the sum of products of degrees of pairs of adjacent vertices. In this paper, we investigate the first and the second Zagreb indices of maximal outerplanar graph. We determine sharp upper and lower bounds for M 1-, M 2-values among the n-vertex maximal outerplanar graphs. As well we determine sharp upper and lower bounds of Zagreb indices for n-vertex outerplanar graphs (resp. maximal outerplanar graphs) with perfect matchings.