On Sombor Index

Kinkar Das; Ahmet Çevik; Ismail Cangul; Yilun Shang

doi:10.3390/sym13010140

On Sombor Index

Kinkar Das^*, Ahmet Çevik, Ismail Cangul, Yilun Shang^*

^*Corresponding author for this work

Computer and Information Sciences Department

Research output: Contribution to journal › Article › peer-review

130 Citations (Scopus)

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Abstract

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO = SO(G) = ∑ √d _G (v _i) ² + d _G (v _j) ², where d _G (v _i) is the degree of vertex v _i in G. Here, v _i v _j ∈E(G) we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

Original language	English
Article number	140
Pages (from-to)	1-12
Number of pages	12
Journal	Symmetry
Volume	13
Issue number	1
DOIs	https://doi.org/10.3390/sym13010140
Publication status	Published - 16 Jan 2021

Keywords

Graph
Independence number
Maximum degree
Minimum degree
Sombor index

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10.3390/sym13010140Licence: CC BY

On Sombor IndexFinal published version, 253 KBLicence: CC BY

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abstract = "The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO = SO(G) = ∑ √d G (v i) 2 + d G (v j) 2, where d G (v i) is the degree of vertex v i in G. Here, v i v j ∈E(G) we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work. ",

keywords = "Graph, Independence number, Maximum degree, Minimum degree, Sombor index",

author = "Kinkar Das and Ahmet {\c C}evik and Ismail Cangul and Yilun Shang",

note = "Funding Information: Funding: This research was funded by Northumbria University under No. 201920A1001.",

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AU - Das, Kinkar

AU - Çevik, Ahmet

AU - Cangul, Ismail

AU - Shang, Yilun

N1 - Funding Information: Funding: This research was funded by Northumbria University under No. 201920A1001.

PY - 2021/1/16

Y1 - 2021/1/16

N2 - The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO = SO(G) = ∑ √d G (v i) 2 + d G (v j) 2, where d G (v i) is the degree of vertex v i in G. Here, v i v j ∈E(G) we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

AB - The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO = SO(G) = ∑ √d G (v i) 2 + d G (v j) 2, where d G (v i) is the degree of vertex v i in G. Here, v i v j ∈E(G) we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

KW - Graph

KW - Independence number

KW - Maximum degree

KW - Minimum degree

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JO - Symmetry

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On Sombor Index

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Keywords

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