Quasi-tree graphs with the minimal Sombor indices

Li, Yibo, Liu, Huiqing, and Zhang, Ruiting. "Quasi-tree graphs with the minimal Sombor indices." Czechoslovak Mathematical Journal 72.4 (2022): 1227-1238. <http://eudml.org/doc/298892>.

@article{Li2022,
abstract = {The Sombor index $SO(G)$ of a graph $G$ is the sum of the edge weights $\sqrt\{d^2_G(u)+d^2_G(v)\}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of the vertex $u$ in $G$. A connected graph $G = (V ,E)$ is called a quasi-tree if there exists $u\in V (G)$ such that $G-u$ is a tree. Denote $\mathcal \{Q\}(n,k)=\lbrace G \colon G$ is a quasi-tree graph of order $n$ with $G-u$ being a tree and $d_G(u)=k\rbrace $. We determined the minimum and the second minimum Sombor indices of all quasi-trees in $\mathcal \{Q\}(n,k)$. Furthermore, we characterized the corresponding extremal graphs, respectively.},
author = {Li, Yibo, Liu, Huiqing, Zhang, Ruiting},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sombor index; quasi-tree; tree},
language = {eng},
number = {4},
pages = {1227-1238},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Quasi-tree graphs with the minimal Sombor indices},
url = {http://eudml.org/doc/298892},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Li, Yibo
AU - Liu, Huiqing
AU - Zhang, Ruiting
TI - Quasi-tree graphs with the minimal Sombor indices
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 4
SP - 1227
EP - 1238
AB - The Sombor index $SO(G)$ of a graph $G$ is the sum of the edge weights $\sqrt{d^2_G(u)+d^2_G(v)}$ of all edges $uv$ of $G$, where $d_G(u)$ denotes the degree of the vertex $u$ in $G$. A connected graph $G = (V ,E)$ is called a quasi-tree if there exists $u\in V (G)$ such that $G-u$ is a tree. Denote $\mathcal {Q}(n,k)=\lbrace G \colon G$ is a quasi-tree graph of order $n$ with $G-u$ being a tree and $d_G(u)=k\rbrace $. We determined the minimum and the second minimum Sombor indices of all quasi-trees in $\mathcal {Q}(n,k)$. Furthermore, we characterized the corresponding extremal graphs, respectively.
LA - eng
KW - Sombor index; quasi-tree; tree
UR - http://eudml.org/doc/298892
ER -