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...
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| Language: | English |
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Elsevier
2024-12-01
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| Series: | Examples and Counterexamples |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666657X24000247 |
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| 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 |