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arXiv · 1801.03885

Zeroth-order general Randi\`c index of $k$-generalized quasi trees

M. K. Jamil·I. Tomescu
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Abstract

For a simple graph $G(V,E)$, the zeroth-order general Randi\' c index is defined as $^0R_{\alpha}(G)=\sum_{v\in V(G)}d(v)^{\alpha}$, where $d(v)$ is the degree of the vertex $v$ and $\alpha\ne0$ is a real number. The $k$-generalized quasi-tree is a connected graph $G$ with a subset $V_k\subset V(G)$, where $|V_k|=k$ such that $G-V_k$ is a tree, but for any subset $V_{k-1}\subset V(G)$ with cardinality $k-1$, $G-V_{k-1}$ is not a tree. In this paper, we characterize the extremal $k$-generalized quasi trees with the minimum and maximum values of the zeroth-order general Randi\' c index for $\alpha\neq 0$.

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M. K. Jamil, I. Tomescu. 2018-01-11. Zeroth-order general Randi\`c index of $k$-generalized quasi trees. https://arxiv.org/abs/1801.03885

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