TY - JOUR
T1 - Proof of a conjecture on communicability distance sum index of graphs
AU - Huang, Xueyi
AU - Das, Kinkar Chandra
N1 - Publisher Copyright:
© 2022 Elsevier Inc.
PY - 2022/7/15
Y1 - 2022/7/15
N2 - Let G be a connected graph with adjacency matrix A, and let A=exp(A). The communicability distance between two vertices u and v of G is defined as ξuv=(Auu+Avv−2Auv)1/2, and the communicability distance sum index (CDS index for short) of G is the sum of all communicability distances between vertices of G. In this paper, it is shown that the complete graph Kn is the unique graph attaining the minimum CDS index among all connected graphs of order n. This confirms a conjecture of Estrada (2012) [2]. Furthermore, some upper and lower bounds for the CDS index of graphs are provided.
AB - Let G be a connected graph with adjacency matrix A, and let A=exp(A). The communicability distance between two vertices u and v of G is defined as ξuv=(Auu+Avv−2Auv)1/2, and the communicability distance sum index (CDS index for short) of G is the sum of all communicability distances between vertices of G. In this paper, it is shown that the complete graph Kn is the unique graph attaining the minimum CDS index among all connected graphs of order n. This confirms a conjecture of Estrada (2012) [2]. Furthermore, some upper and lower bounds for the CDS index of graphs are provided.
KW - Communicability distance
KW - Communicability distance sum index
KW - Graph eigenvalues
KW - Lagrange multiplier theorem
KW - Spectral decomposition
UR - https://www.scopus.com/pages/publications/85127502372
U2 - 10.1016/j.laa.2022.03.027
DO - 10.1016/j.laa.2022.03.027
M3 - Article
AN - SCOPUS:85127502372
SN - 0024-3795
VL - 645
SP - 278
EP - 292
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -