Some extremal graphs with respect to sombor index

Kinkar Chandra Das; Yilun Shang

doi:10.3390/math9111202

Some extremal graphs with respect to sombor index

Kinkar Chandra Das
, Yilun Shang

Department of Mathematics

Northumbria University

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

56 Scopus citations

Abstract

Let G be a graph with set of vertices V(G) (|V(G)| = n) and edge set E(G). Very recently, a new degree-based molecular structure √ descriptor, called Sombor index is denoted by SO(G) and is defined as SO = SO(G) = ∑ d_G (v_i )² + d_G (v_j )², where d_G (v_i ) is the degree of the vertex v_i v_i v_j ∈E(G) in G. In this paper we present some lower and upper bounds on the Sombor index of graph G in terms of graph parameters (clique number, chromatic number, number of pendant vertices, etc.) and characterize the extremal graphs.

Original language	English
Article number	1202
Journal	Mathematics
Volume	9
Issue number	11
DOIs	https://doi.org/10.3390/math9111202
State	Published - 1 Jun 2021

Keywords

Chromatic number
Clique number
Graph
Sombor index

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10.3390/math9111202

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abstract = "Let G be a graph with set of vertices V(G) (|V(G)| = n) and edge set E(G). Very recently, a new degree-based molecular structure √ descriptor, called Sombor index is denoted by SO(G) and is defined as SO = SO(G) = ∑ dG (vi )2 + dG (vj )2, where dG (vi ) is the degree of the vertex vi vi vj ∈E(G) in G. In this paper we present some lower and upper bounds on the Sombor index of graph G in terms of graph parameters (clique number, chromatic number, number of pendant vertices, etc.) and characterize the extremal graphs.",

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N2 - Let G be a graph with set of vertices V(G) (|V(G)| = n) and edge set E(G). Very recently, a new degree-based molecular structure √ descriptor, called Sombor index is denoted by SO(G) and is defined as SO = SO(G) = ∑ dG (vi )2 + dG (vj )2, where dG (vi ) is the degree of the vertex vi vi vj ∈E(G) in G. In this paper we present some lower and upper bounds on the Sombor index of graph G in terms of graph parameters (clique number, chromatic number, number of pendant vertices, etc.) and characterize the extremal graphs.

AB - Let G be a graph with set of vertices V(G) (|V(G)| = n) and edge set E(G). Very recently, a new degree-based molecular structure √ descriptor, called Sombor index is denoted by SO(G) and is defined as SO = SO(G) = ∑ dG (vi )2 + dG (vj )2, where dG (vi ) is the degree of the vertex vi vi vj ∈E(G) in G. In this paper we present some lower and upper bounds on the Sombor index of graph G in terms of graph parameters (clique number, chromatic number, number of pendant vertices, etc.) and characterize the extremal graphs.

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KW - Clique number

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Some extremal graphs with respect to sombor index

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Keywords

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