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- W4380715265 abstract "Let $G$ be a graph with adjacency matrix $A(G)$ and let $D(G)$ be the diagonal matrix of vertex degrees of $G$. For any real $alpha in [0,1]$, Nikiforov defined the $A_alpha$-matrix of a graph $G$ as $A_alpha(G)=alpha D(G)+(1-alpha)A(G)$. The largest eigenvalue of $A_alpha(G)$ is called the $alpha$-index or the $A_alpha$-spectral radius of $G$. A graph is minimally $k$-(edge)-connected if it is $k$-(edge)-connected and deleting any arbitrary chosen edge always leaves a graph which is not $k$-(edge)-connected. In this paper, we characterize the minimally 2-edge-connected graphs and minimally 3-connected graph with given order having the maximum $alpha$-index for $alpha in [frac{1}{2},1)$, respectively." @default.
- W4380715265 created "2023-06-15" @default.
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- W4380715265 date "2023-06-13" @default.
- W4380715265 modified "2023-09-23" @default.
- W4380715265 title "On the $alpha$-index of minimally $k$-(edge-)connected graphs for small $k$" @default.
- W4380715265 doi "https://doi.org/10.48550/arxiv.2306.07793" @default.
- W4380715265 hasPublicationYear "2023" @default.
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