\(a_\alpha \)-spectral radius of the second power of a graph. (English) Zbl 1428.05185
Summary: The \(k\) th power of a graph \(G\), denoted by \(G^k\), is a graph with the same set of vertices as \(G\) such that two vertices are adjacent in \(G^k\) if and only if their distance in \(G\) is at most \(k\). In this paper, we give upper and lower bounds on the \(A_\alpha \)-spectral radius of \(G^2\). Furthermore, the first three largest \(A_\alpha \)-spectral radius of the second power of trees are determined.
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