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Sharp bounds for Zagreb indices of maximal outerplanar graphs

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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.

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China

    Ailin Hou & Shuchao Li

  2. Department of Mathematics, University of Mississippi University, Oxford, MS, 38677, USA

    Lanzhen Song & Bing Wei

Authors
  1. Ailin Hou
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  2. Shuchao Li
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  3. Lanzhen Song
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  4. Bing Wei
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Corresponding author

Correspondence to Shuchao Li.

Additional information

Partially supported by Hubei Key Laboratory of Mathematical Sciences and the CCNU Project.

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Hou, A., Li, S., Song, L. et al. Sharp bounds for Zagreb indices of maximal outerplanar graphs. J Comb Optim 22, 252–269 (2011). https://doi.org/10.1007/s10878-010-9288-8

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