Sharp bounds for Zagreb indices of maximal outerplanar graphs

Ailin Hou (), Shuchao Li (), Lanzhen Song and Bing Wei ()
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Ailin Hou: Central China Normal University
Shuchao Li: Central China Normal University
Lanzhen Song: University of Mississippi University
Bing Wei: University of Mississippi University

Journal of Combinatorial Optimization, 2011, vol. 22, issue 2, No 9, 252-269

Abstract: 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.

Keywords: Zagreb index; Maximal outerplanar graph; Perfect matching (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10878-010-9288-8

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