The spectral closeness of a graph G is defined as the spectral radius of the closeness matrix of G, whose (u, v)-entry for vertex u and vertex v is if u ≠ v and 0 otherwise, where d$$(u, v) is the distance between u and v in G. The residual spectral closeness of a nontrivial graph G is defined as the minimum spectral closeness of the subgraphs of G with one vertex deleted. We propose local grafting operations that decrease or increase the spectral closeness and determine those graphs that uniquely minimize and/or maximize the spectral closeness in some families of graphs. We also discuss extremal properties of the residual spectral closeness.
Keywords: Spectral closeness, residual spectral closeness, local grafting operation, extremal graph
@article{RO_2022__56_4_2651_0,
author = {Zheng, Lu and Zhou, Bo},
title = {On the spectral closeness and residual spectral closeness of graphs},
journal = {RAIRO. Operations Research},
pages = {2651--2668},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {4},
doi = {10.1051/ro/2022125},
mrnumber = {4469509},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022125/}
}
TY - JOUR AU - Zheng, Lu AU - Zhou, Bo TI - On the spectral closeness and residual spectral closeness of graphs JO - RAIRO. Operations Research PY - 2022 SP - 2651 EP - 2668 VL - 56 IS - 4 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022125/ DO - 10.1051/ro/2022125 LA - en ID - RO_2022__56_4_2651_0 ER -
Zheng, Lu; Zhou, Bo. On the spectral closeness and residual spectral closeness of graphs. RAIRO. Operations Research, Tome 56 (2022) no. 4, pp. 2651-2668. doi: 10.1051/ro/2022125
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