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Sharp bounds of the Zagreb indices of k-trees

Author

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  • John Estes

    (University of Mississippi)

  • Bing Wei

    (University of Mississippi)

Abstract

For a graph G, 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 the products of degrees of pairs of adjacent vertices. The Zagreb indices have been the focus of considerable research in computational chemistry dating back to Gutman and Trinajstić in 1972. In 2004, Das and Gutman determined sharp upper and lower bounds for M 1 and M 2 values for trees along with the unique trees that obtain the minimum and maximum M 1 and M 2 values respectively. In this paper, we generalize the results of Das and Gutman to the generalized tree, the k-tree, where the results of Das and Gutman are for k=1. Also by showing that maximal outerplanar graphs are 2-trees, we also extend a result of Hou, Li, Song, and Wei who determined sharp upper and lower bounds for M 1 and M 2 values for maximal outerplanar graphs.

Suggested Citation

  • John Estes & Bing Wei, 2014. "Sharp bounds of the Zagreb indices of k-trees," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 271-291, February.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:2:d:10.1007_s10878-012-9515-6
    DOI: 10.1007/s10878-012-9515-6
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    References listed on IDEAS

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    1. Ailin Hou & Shuchao Li & Lanzhen Song & Bing Wei, 2011. "Sharp bounds for Zagreb indices of maximal outerplanar graphs," Journal of Combinatorial Optimization, Springer, vol. 22(2), pages 252-269, August.
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    Cited by:

    1. Shaohui Wang & Zehui Shao & Jia-Bao Liu & Bing Wei, 2019. "The Bounds of Vertex Padmakar–Ivan Index on k -Trees," Mathematics, MDPI, vol. 7(4), pages 1-10, April.
    2. Lkhagva Buyantogtokh & Batmend Horoldagva & Kinkar Chandra Das, 2020. "On reduced second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 776-791, April.

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