论文标题
图表的最高度和光谱半径
Maximum degree and spectral radius of graphs in terms of size
论文作者
论文摘要
关于图形图理论中重要的研究项目，对图形的（无标志性Laplacian）光谱半径的关系研究。分别用$ρ（g）$和$ q（g）$表示频谱半径和无标志性的laplacian光谱半径。令$ k \ ge 0 $为固定整数，而$ g $是大小$ m $的图。我们表明，如果$ρ（g）\ ge \ sqrt {m-k} $，则$ c_4 \ subseteq g $或$ k_ {1，m-k} \ subseteq g $。此外，我们证明，如果$ q（g）\ ge m-k $，则$ k_ {1，m-k} \ subseteq g $。这两个结果都扩大了一些已知结果。
Research on the relationship of the (signless Laplacian) spectral radius of a graph with its structure properties is an important research project in spectral graph theory. Denote by $ρ(G)$ and $q(G)$ the spectral radius and the signless Laplacian spectral radius of a graph $G$, respectively. Let $k\ge 0$ be a fixed integer and $G$ be a graph of size $m$ which is large enough. We show that if $ρ(G)\ge\sqrt{m-k}$, then $C_4\subseteq G$ or $K_{1,m-k}\subseteq G$. Furthermore, we prove that if $q(G)\ge m-k$, then $K_{1,m-k}\subseteq G$. Both these two results extend some known results.
