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Sharp bounds for Zagreb indices of maximal outerplanar graphs

Author

Listed:
  • Ailin Hou

    (Central China Normal University)

  • Shuchao Li

    (Central China Normal University)

  • Lanzhen Song

    (University of Mississippi University)

  • Bing Wei

    (University of Mississippi University)

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.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:2:d:10.1007_s10878-010-9288-8
    DOI: 10.1007/s10878-010-9288-8
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    Citations

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    Cited by:

    1. Shuchao Li & Licheng Zhang & Minjie Zhang, 2019. "On the extremal cacti of given parameters with respect to the difference of zagreb indices," Journal of Combinatorial Optimization, Springer, vol. 38(2), pages 421-442, August.
    2. 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.
    3. Shuchao Li & Huihui Zhang & Minjie Zhang, 2016. "Further results on the reciprocal degree distance of graphs," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 648-668, February.
    4. Lifang Zhao & Hongshuai Li & Yuping Gao, 2020. "On the extremal graphs with respect to the total reciprocal edge-eccentricity," Journal of Combinatorial Optimization, Springer, vol. 39(1), pages 115-137, January.
    5. 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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