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On the Extremal Zagreb Indices of Graphs with Cut Edges

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An Erratum to this article was published on 09 February 2010

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 show that all connected graphs with n vertices and k cut edges, the maximum (resp. minimum) M 1- and M 2-value are obtained, respectively, and uniquely, at K k n (resp. P k n ), where K k n is a graph obtained by joining k independent vertices to one vertex of K n−k and P k n is a graph obtained by connecting a pendent path P k+1 to one vertex of C n−k.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Yanqin Feng & Xia Hu

  2. Faculty of Mathematics and Statistics, Hubei Key Laboratory of Mathematical Science, Central China Normal University, Wuhan, 430079, China

    Shuchao Li

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  1. Yanqin Feng
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  2. Xia Hu
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  3. Shuchao Li
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Correspondence to Shuchao Li.

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An erratum to this article can be found at http://dx.doi.org/10.1007/s10440-010-9566-6

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Feng, Y., Hu, X. & Li, S. On the Extremal Zagreb Indices of Graphs with Cut Edges. Acta Appl Math 110, 667–684 (2010). https://doi.org/10.1007/s10440-009-9467-8

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