论文标题
算术图算术光谱半径
Arithmetic-Geometric spectral radii of Unicyclic graphs
论文作者
论文摘要
令$ d_ {v_ {i}} $为$ g $的顶点$ v_ {i} $的程度。图$ g $的算术几何矩阵$ a_ {ag}（g）$是一个方形矩阵，其中$（i，j）$ - 条目等于$ \ displayStyle \ frac {d_ {v_ {i}}+d_ {v_ {v_ {j}}} {2 \ sqrt {d_ {d_ {v_ {i}} d_ {v_ {v_ {j {j}}}}} $，如果vertices $ v_ {i} $ v_ and joutt和$ v_} $ρ_{ag}（g）$表示的算术几何光谱半径是$ g $的，是算术 - 几何矩阵$ a_ {ag}（g）$的最大特征值。在本文中，确定了最小和前四个最大算术光谱半径的订单$ n \ geq5 $的单车图。
Let $d_{v_{i}}$ be the degree of the vertex $v_{i}$ of $G$. The arithmetic-geometric matrix $A_{ag}(G)$ of a graph $G$ is a square matrix, where the $(i,j)$-entry is equal to $\displaystyle \frac{d_{v_{i}}+d_{v_{j}}}{2\sqrt{d_{v_{i}}d_{v_{j}}}}$ if the vertices $v_{i}$ and $v_{j}$ are adjacent, and 0 otherwise. The arithmetic-geometric spectral radius of $G$, denoted by $ρ_{ag}(G)$, is the largest eigenvalue of the arithmetic-geometric matrix $A_{ag}(G)$. In this paper, the unicyclic graphs of order $n\geq5$ with the smallest and first four largest arithmetic-geometric spectral radii are determined.
