Distance between distance spectra of graphs

作者：Lin, Huiqiu^*; Li, Dan; Das, Kinkar Ch.

来源：Linear and Multilinear Algebra, 2017, 65(12): 2538-2550.

DOI：10.1080/03081087.2017.1278737

• Distance spectra
• distance matrix
• cospectral
• distance

Let G = (V, E) be a connected graph with vertex set V(G) = {v(1), v(2), ... , v(n)} and edge set E(G). Let D(G) be the distance matrix of G and lambda(1)(D) >= ... >= lambda(n)(D) be its distance spectrum. The distance between distance spectra of G and G' is defined by @@@ sigma(G, G') = Sigma(n)(i=1)vertical bar lambda(i)(D(G)) - lambda(i)(D(G'))vertical bar. @@@ Define the cospectrality of G by @@@ cs(G) = min{Sigma(n)(i=1)vertical bar lambda(i)(D(G)) - lambda(i)(D(G'))vertical bar : G' not isomorphic to G}. @@@ Let cs(n) = max{cs(G) : G a connected graph on n vertices}. In the paper, we obtain lower bounds on sigma(G, K-n) and sigma(G, K-a,K-b) for a + b = n. Furthermore, we give an upper bound on cs(n).

• 出版日期2017
• 单位华东理工大学; 新疆大学