On digraphs with maximum first outdegree Zagreb index

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Government Degree College Uri, Kashmir, India

2 Department of Mathematics, University of Kashmir, India

Abstract

Let $D$ be a digraph with order $n$ and $a$ arcs. Let $d_1^{+}, d_2^{+},\dots, d_n^{+}$ be the vertex outdegrees of $D$. The first outdegree Zagreb index of $D$ is denoted by $Zg^{+}(D)$ and is defined as $Zg^{+}D)=\sum\limits_{i=1}^{n}(d_i^{+})^2$. In this paper, we completely characterize the oriented graphs which attain the maximum value for the first outdegree Zagreb index $Zg^{+}(D)$ among all connected oriented graphs $D$ of order $n$ with $n-1\le a\le 2n-3$. Further, we determine the oriented graphs which attain the second maximum value for $Zg^{+}(D)$ among all oriented graphs of order $n$ with $n-1\le a\le n+2$. We consider the problem of determining the orientations which attain the maximum and the minimum values for the first outdegree Zagreb index for the Path, the Cycle and the Star.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 05 November 2025

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