On Sombor index and graph energy of some chemically important graphs

Sombor index of a graph G=(V(G),E(G)) is provided by the expression ∑uv∈E(G)du2+dv2, where dx is the degree of the vertex x∈V(G). The energy of a graph is the quantity given by the total of the absolute values of its adjacency matrix’s eigenvalues. In this article, we improve the relation between th...

Full description

Saved in:
Bibliographic Details
Main Authors: Md Selim Reja, Sk. Md. Abu Nayeem
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Examples and Counterexamples
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666657X24000247
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850122304891125760
author Md Selim Reja
Sk. Md. Abu Nayeem
author_facet Md Selim Reja
Sk. Md. Abu Nayeem
author_sort Md Selim Reja
collection DOAJ
description Sombor index of a graph G=(V(G),E(G)) is provided by the expression ∑uv∈E(G)du2+dv2, where dx is the degree of the vertex x∈V(G). The energy of a graph is the quantity given by the total of the absolute values of its adjacency matrix’s eigenvalues. In this article, we improve the relation between the Sombor index and graph energy and derive the relation between them for unicyclic, bicyclic and tricyclic graphs, trees, triangular chain, square cactus chain and hexagonal cactus chain graphs. At last, we find the bounds of graph energy for zigzag and linear hexagonal chains.
format Article
id doaj-art-0a513f3d4d5d4d9283f43ced060d3ea8
institution OA Journals
issn 2666-657X
language English
publishDate 2024-12-01
publisher Elsevier
record_format Article
series Examples and Counterexamples
spelling doaj-art-0a513f3d4d5d4d9283f43ced060d3ea82025-08-20T02:34:52ZengElsevierExamples and Counterexamples2666-657X2024-12-01610015810.1016/j.exco.2024.100158On Sombor index and graph energy of some chemically important graphsMd Selim Reja0Sk. Md. Abu Nayeem1Department of Mathematics and Statistics, Aliah University, Kolkata, 700 160, IndiaCorresponding author.; Department of Mathematics and Statistics, Aliah University, Kolkata, 700 160, IndiaSombor index of a graph G=(V(G),E(G)) is provided by the expression ∑uv∈E(G)du2+dv2, where dx is the degree of the vertex x∈V(G). The energy of a graph is the quantity given by the total of the absolute values of its adjacency matrix’s eigenvalues. In this article, we improve the relation between the Sombor index and graph energy and derive the relation between them for unicyclic, bicyclic and tricyclic graphs, trees, triangular chain, square cactus chain and hexagonal cactus chain graphs. At last, we find the bounds of graph energy for zigzag and linear hexagonal chains.http://www.sciencedirect.com/science/article/pii/S2666657X24000247Sombor indexGraph energyUnicyclic graphBicyclic graphHexagonal chainChain of triangles
spellingShingle Md Selim Reja
Sk. Md. Abu Nayeem
On Sombor index and graph energy of some chemically important graphs
Examples and Counterexamples
Sombor index
Graph energy
Unicyclic graph
Bicyclic graph
Hexagonal chain
Chain of triangles
title On Sombor index and graph energy of some chemically important graphs
title_full On Sombor index and graph energy of some chemically important graphs
title_fullStr On Sombor index and graph energy of some chemically important graphs
title_full_unstemmed On Sombor index and graph energy of some chemically important graphs
title_short On Sombor index and graph energy of some chemically important graphs
title_sort on sombor index and graph energy of some chemically important graphs
topic Sombor index
Graph energy
Unicyclic graph
Bicyclic graph
Hexagonal chain
Chain of triangles
url http://www.sciencedirect.com/science/article/pii/S2666657X24000247
work_keys_str_mv AT mdselimreja onsomborindexandgraphenergyofsomechemicallyimportantgraphs
AT skmdabunayeem onsomborindexandgraphenergyofsomechemicallyimportantgraphs