کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6423584 | 1342425 | 2011 | 7 صفحه PDF | دانلود رایگان |
Let D(G)=(di,j)nÃn denote the distance matrix of a connected graph G with order n, where dij is equal to the distance between vi and vj in G. The largest eigenvalue of D(G) is called the distance spectral radius of graph G, denoted by ϱ(G). In this paper, we give some graft transformations that decrease and increase ϱ(G) and prove that the graph Snâ² (obtained from the star Sn on n (n is not equal to 4, 5) vertices by adding an edge connecting two pendent vertices) has minimal distance spectral radius among unicyclic graphs on n vertices; while Pnâ² (obtained from a triangle K3 by attaching pendent path Pnâ3 to one of its vertices) has maximal distance spectral radius among unicyclic graphs on n vertices.
⺠Some new graft transformations that increase distance spectral radius are presented. ⺠Graphs with minimal distance spectral radius among unicyclic graphs are determined. ⺠Graphs with maximal distance spectral radius among unicyclic graphs are determined.
Journal: Discrete Mathematics - Volume 311, Issue 20, 28 October 2011, Pages 2117-2123