Bounds on the \(\alpha \)-distance energy and \(\alpha \)-distance Estrada index of graphs (Q2188026)

Summary: Let \(G\) be a simple undirected connected graph, then \(D_\alpha\left( G\right)=\alpha Tr\left( G\right)+\left( 1 - \alpha\right)D\left( G\right)\) is called the \(\alpha \)-distance matrix of \(G\), where \(\alpha\in\left[ 0,1\right]\), \(D\left( G\right)\) is the distance matrix of \(G\), and \(Tr\left( G\right)\) is the vertex transmission diagonal matrix of \(G\). In this paper, we study some bounds on the \(\alpha \)-distance energy and \(\alpha \)-distance Estrada index of \(G\). Furthermore, we establish the relation between \(\alpha \)-distance Estrada index and \(\alpha \)-distance energy.