ESTRADA INDEX OF GENERAL WEIGHTED GRAPHS
ESTRADA INDEX OF GENERAL WEIGHTED GRAPHS
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DOI：
10.1017/s0004972712000676
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发表时间：
2013-07
影响因子：
0.7
通讯作者：
Y. Shang
中科院分区：
文献类型：
--
作者：
Y. Shang
设$G$是$n$顶点上的一般赋权图(可能有自环)，$\lambda_1，\lambda_2，\cdots，\lambda_n$是它的特征值。$G$的Estrada指标是一个图不变量，定义为$EE=\sum_{i=1}^ne^{\lambda_i}$。我们给出了基于闭游程在$G$中的权重的$EE$的一般表达式。我们用涉及闭步行权的低阶谱矩建立了$EE$的上下界。给出了一个具体的计算实例。10.1017/S0004972712000676
Let $G$ be a general weighted graph (with possible self-loops) on $n$ vertices and $\lambda_1,\lambda_2,\cdots,\lambda_n$ be its eigenvalues. The Estrada index of $G$ is a graph invariant defined as $EE=\sum_{i=1}^ne^{\lambda_i}$. We present a generic expression for $EE$ based on weights of closed walks in $G$. We establish lower and upper bounds for $EE$ in terms of low-order spectral moments involving the weights of closed walks. A concrete example of calculation is provided. 10.1017/S0004972712000676