On Sombor index of trees

Kinkar Chandra Das; Ivan Gutman

doi:10.1016/j.amc.2021.126575

On Sombor index of trees

Kinkar Chandra Das
, Ivan Gutman

Department of Mathematics

University of Kragujevac

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

78 Scopus citations

Abstract

This paper is concerned with the recently introduced Sombor index SO, defined as SO=SO(G)=∑v_kv_ℓ∈E(G)d_G(v_k)²+d_G(v_ℓ)²,where d_G(v) is the degree of the vertex v of a graph G. We present bounds on SO of trees in terms of order, independence number, and number of pendent vertices, and characterize the extremal cases. In addition, analogous results for quasi-trees are established.

Original language	English
Article number	126575
Journal	Applied Mathematics and Computation
Volume	412
DOIs	https://doi.org/10.1016/j.amc.2021.126575
State	Published - Jan 2022

Keywords

Independence number
Majorization
Quasi-tree
Sombor index
Tree

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abstract = "This paper is concerned with the recently introduced Sombor index SO, defined as SO=SO(G)=∑vkvℓ∈E(G)dG(vk)2+dG(vℓ)2,where dG(v) is the degree of the vertex v of a graph G. We present bounds on SO of trees in terms of order, independence number, and number of pendent vertices, and characterize the extremal cases. In addition, analogous results for quasi-trees are established.",

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AB - This paper is concerned with the recently introduced Sombor index SO, defined as SO=SO(G)=∑vkvℓ∈E(G)dG(vk)2+dG(vℓ)2,where dG(v) is the degree of the vertex v of a graph G. We present bounds on SO of trees in terms of order, independence number, and number of pendent vertices, and characterize the extremal cases. In addition, analogous results for quasi-trees are established.

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KW - Majorization

KW - Quasi-tree

KW - Sombor index

KW - Tree

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JO - Applied Mathematics and Computation

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On Sombor index of trees

Abstract

Keywords

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