论文标题
非单个图的能量的下限在平均程度上
A lower bound of the energy of non-singular graphs in terms of average degree
论文作者
论文摘要
令$ g $为订单$ n $，带有邻接矩阵$ a（g）$。图$ g $的\ textIt {energy}，用$ \ mathcal {e}（g）$表示为$ a（g）$的特征值的绝对值之和。据推测，如果$ a（g）$是非符号的，则$ \ mathcal {e}（g）\geqΔ（g）+δ（g）$。在本文中，我们提出了一个更强有力的猜想，例如$ n \ geq 5 $，$ \ mathcal {e}（g）\ geq n-1+ d $，其中$ d $是$ g $的平均度。在这里，我们表明猜想适用于二分图，平面图和$ d \ leq n -2 \ ln n -3 $的图形
Let $G$ be a graph of order $n$ with adjacency matrix $A(G)$. The \textit{energy} of graph $G$, denoted by $\mathcal{E}(G)$, is defined as the sum of absolute value of eigenvalues of $A(G)$. It was conjectured that if $A(G)$ is non-singular, then $\mathcal{E}(G)\geqΔ(G)+δ(G)$. In this paper we propose a stronger conjecture as for $n \geq 5$, $\mathcal{E}(G)\geq n-1+ d$, where $d$ is the average degree of $G$. Here, we show that conjecture holds for bipartite graphs, planar graphs and for the graphs with $d \leq n-2\ln n -3$
