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arXiv · 2211.05218

Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices

Tariq A. Alraqad·Igor Z. Milovanovic·Hicham Saber·Akbar Ali·Jaya Percival Mazorodze·Adel A. Attiya
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Abstract

Let $d_u$ be the degree of a vertex $u$ of a graph $G$. The atom-bond sum-connectivity (ABS) index of a graph $G$ is the sum of the numbers $(1-2(d_v+d_w)^{-1})^{1/2}$ over all edges $vw$ of $G$. This paper gives the characterization of the graph possessing the minimum ABS index in the class of all trees of a fixed number of pendent vertices; the star is the unique extremal graph in the mentioned class of graphs. The problem of determining graphs possessing the minimum ABS index in the class of all trees with $n$ vertices and $p$ pendent vertices is also addressed; such extremal trees have the maximum degree $3$ when $n\ge 3p-2\ge7$, and the balanced double star is the unique such extremal tree for the case $p=n-2$.

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Tariq A. Alraqad, Igor Z. Milovanovic, Hicham Saber, Akbar Ali, Jaya Percival Mazorodze, Adel A. Attiya. 2022-11-09. Minimum Atom-Bond Sum-Connectivity Index of Trees With a Fixed Order and/or Number of Pendent Vertices. https://arxiv.org/abs/2211.05218

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