论文标题
在$α$ -ADJACENCY的图形和Zagreb索引
On $α$-adjacency energy of graphs and Zagreb index
论文作者
论文摘要
令$ a（g）$为邻接矩阵，$ d（g）$是简单连接的图形$ g $的顶点度的对角线矩阵。 Nikiforov将$ d（g）$和$ a（g）$的矩阵$a_α（g）$定义为$a_α（g）=αd（g）+（g）+（1-α）a（g）$，价格为$ 0 \ leqleqα\ leq 1 $。如果$ρ_{1} \ geqρ_{2} \ geq \ dots \ geqρ_{n} $是$a_α（g）$的特征（我们称之为$α$α$ -AdjAcency eigenvalues of $ g $） $ e^{a_α}（g）= \ sum_ {i = 1}^{n} \ left |ρ_i-\ frac {2αm} {n} {n} \ right | $，其中$ n $是订单，$ m $是$ g $的大小。我们以$ n $，$ n $，$ m $和ZAGREB索引$ zg（g）$相关的结构相关的$ n $，尺寸$ n $，$ e^{a_α}（g）$的上限和下限。此外，我们表征了达到这些边界的极端图。
Let $A(G)$ be the adjacency matrix and $D(G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$. Nikiforov defined the matrix $A_α(G)$ of the convex combinations of $D(G)$ and $A(G)$ as $A_α(G)=αD(G)+(1-α)A(G)$, for $0\leq α\leq 1$. If $ ρ_{1}\geq ρ_{2}\geq \dots \geq ρ_{n}$ are the eigenvalues of $A_α(G)$ (which we call $α$-adjacency eigenvalues of $G$), the $ α$-adjacency energy of $G$ is defined as $E^{A_α}(G)=\sum_{i=1}^{n}\left|ρ_i-\frac{2αm}{n}\right|$, where $n$ is the order and $m$ is the size of $G$. We obtain the upper and lower bounds for $E^{A_α}(G) $ in terms of order $n$, size $m$ and Zagreb index $Zg(G)$ associated to the structure of $G$. Further, we characterize the extremal graphs attaining these bounds.
