倒数距离无符号拉普拉斯极值图

The Extremal Graph of the Reciprocal Distance Signless Laplacian Matrix

摘要: 给定图 G 是简单无向连通图，RD(G) 表示图 G 的 Harary 矩阵，也称为图 G 的倒数距离矩阵。图 G 的倒数距离无符号拉普拉斯矩阵定义为 RQ(G) = RT (G) + RD(G)，其中 RT (G) 表示图 G 的倒数距离传递度对角矩阵。第二部分刻画了具有固定点数和固定点连通度且有最大倒数距离无符号拉普拉斯谱半径的极值图。第三部分刻画了具有固定点数和固定边连通度且有最大倒数距离无符号拉普拉斯谱半径的极值图。

Abstract: Graph G is a simple undirected connected graph, RD(G) represents the Harary matrix of graph G, which is also the reciprocal distance matrix of graph G. The reciprocal distance signless Laplacian matrix of graph G is defined as RQ(G) = RT (G) + RD(G), where RT (G) represents the reciprocal distance transitivity diagonal matrix of G. The second part describes the extremal graphs with maximal spectral radius of the RQ(G) among all connected graphs of fixed order and fixed vertex connectivity. The third part characterizes the extremal graphs with maximal spectral radius of the RQ(G) among all connected graphs of fixed order and fixed edge connectivity.