论文标题
广义相互距离矩阵的传播
The spread of generalized reciprocal distance matrix
论文作者
论文摘要
广义的相互距离矩阵$rd_α（g）$定义为$rd_α（g）=αrt（g）+（1-α）rd（g），\ quad 0 \ leqleqα\ leq 1. $ $ $ $ $ $ up $λ_{1}（1}（rd_α）（rd_α（rd_α（rd_α）\ geq eqgeq。 \geqλ_{n}（rd_α（g））$是图形$ g $的$rd_α$矩阵的特征值。然后，图$ g $的$rd_α$ -spread可以定义为$ s_ {rd_α}（g）=λ_{1}（rd_α（g）） - λ_{n}（rd_α（g））$。在本文中，我们首先获得了$rd_α$ - 图形的尖锐下限和上限。然后，我们确定具有给定集团数字的$rd_α$ - 分布的$rd_α$ - 分布的下限。最后，我们给出了$rd_α$ - 分布的双星图。我们的结果概括了相互距离矩阵和倒数距离的相关结果。
The generalized reciprocal distance matrix $RD_α(G)$ was defined as $RD_α(G)=αRT(G)+(1-α)RD(G),\quad 0\leq α\leq 1.$ Let $λ_{1}(RD_α(G))\geq λ_{2}(RD_α(G))\geq \cdots \geq λ_{n}(RD_α(G))$ be the eigenvalues of $RD_α$ matrix of graphs $G$. Then the $RD_α$-spread of graph $G$ can be defined as $S_{RD_α}(G)=λ_{1}(RD_α(G))-λ_{n}(RD_α(G))$. In this paper, we first obtain some sharp lower and upper bounds for the $RD_α$-spread of graphs. Then we determine the lower bounds for the $RD_α$-spread of bipartite graphs and graphs with given clique number. At last, we give the $RD_α$-spread of double star graphs. Our results generalize the related results of the reciprocal distance matrix and reciprocal distance signless Laplacian matrix.
