On the Vector Degree Matrix of a Connected Graph
A matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. For some standard graphs, VD-eigenvalues, VD-spectrum, and VD-ener...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/8307871 |
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| _version_ | 1832545926762201088 |
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| author | Nasr A. Zeyada Anwar Saleh Majed Albaity Amr K. Amin |
| author_facet | Nasr A. Zeyada Anwar Saleh Majed Albaity Amr K. Amin |
| author_sort | Nasr A. Zeyada |
| collection | DOAJ |
| description | A matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. For some standard graphs, VD-eigenvalues, VD-spectrum, and VD-energy values are defined and calculated. Moreover, we calculate the VD-matrix and calculate the VD-eigenvalues for graphs representing the chemical composition of paracetamol and tramadol. |
| format | Article |
| id | doaj-art-6ec6ec24b4c4415eaa888afac7113905 |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-6ec6ec24b4c4415eaa888afac71139052025-02-03T07:24:17ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/8307871On the Vector Degree Matrix of a Connected GraphNasr A. Zeyada0Anwar Saleh1Majed Albaity2Amr K. Amin3Department of MathematicsDepartment of MathematicsDepartment of Mathematics Faculty of ScienceDepartment of Mathematics and Computer ScienceA matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. For some standard graphs, VD-eigenvalues, VD-spectrum, and VD-energy values are defined and calculated. Moreover, we calculate the VD-matrix and calculate the VD-eigenvalues for graphs representing the chemical composition of paracetamol and tramadol.http://dx.doi.org/10.1155/2022/8307871 |
| spellingShingle | Nasr A. Zeyada Anwar Saleh Majed Albaity Amr K. Amin On the Vector Degree Matrix of a Connected Graph Journal of Mathematics |
| title | On the Vector Degree Matrix of a Connected Graph |
| title_full | On the Vector Degree Matrix of a Connected Graph |
| title_fullStr | On the Vector Degree Matrix of a Connected Graph |
| title_full_unstemmed | On the Vector Degree Matrix of a Connected Graph |
| title_short | On the Vector Degree Matrix of a Connected Graph |
| title_sort | on the vector degree matrix of a connected graph |
| url | http://dx.doi.org/10.1155/2022/8307871 |
| work_keys_str_mv | AT nasrazeyada onthevectordegreematrixofaconnectedgraph AT anwarsaleh onthevectordegreematrixofaconnectedgraph AT majedalbaity onthevectordegreematrixofaconnectedgraph AT amrkamin onthevectordegreematrixofaconnectedgraph |