论文标题
在$ k $ - 均匀的超级树的$α$ - 光谱半径上
On the $α$-spectral radius of the $k$-uniform supertrees
论文作者
论文摘要
让$ g $为$ k $均匀的超盖，带有顶点套装$ v（g）$和edge set $ e（g）$。连接的和无环的超图称为超级树。 For $0\leqα<1$, the $α$-spectral radius of $G$ is the largest $H$-eigenvalue of $αD(G)+(1-α)A(G)$, where $D(G)$ and $A(G)$ are the diagonal tensor of the degrees and the adjacency tensor of $G$, respectively.在本文中，我们确定了所有$ k $ - 均匀的超级trees中最多$α$ - 均匀半径的独特超级树，其中$ m $边缘和独立性$β$ $ \ lceil \ lceil \ frac {m（k-1）+1} +1} {k} {k} {k} \ rceil \ rceil \leqβ\ leq m $中的序列均与n. $ k $ - 统一的超级树，带有$ M $边缘和匹配的数字$μ$ $ 1 \leqμ\ leq \ leq \ lfloor \ frac {m（k-1）+1} {k} {k} \ rfloor $。
Let $G$ be a $k$-uniform hypergraph with vertex set $V(G)$ and edge set $E(G)$. A connected and acyclic hypergraph is called a supertree. For $0\leqα<1$, the $α$-spectral radius of $G$ is the largest $H$-eigenvalue of $αD(G)+(1-α)A(G)$, where $D(G)$ and $A(G)$ are the diagonal tensor of the degrees and the adjacency tensor of $G$, respectively. In this paper, we determine the unique supertrees with the maximum $α$-spectral radius among all $k$-uniform supertrees with $m$ edges and independence number $β$ for $\lceil\frac{m(k-1)+1}{k}\rceil\leqβ\leq m$, among all $k$-uniform supertrees with given degree sequences, and among all $k$-uniform supertrees with $m$ edges and matching number $μ$ for $1\leqμ\leq\lfloor\frac{m(k-1)+1}{k}\rfloor$, respectively.
