On the Vector Degree Matrix of a Connected Graph | Zendy

Nasr Zeyada | Zendy; Anwar Saleh | Zendy; Majed Albaity | Zendy; Amr Kamel Amin | Zendy

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On the Vector Degree Matrix of a Connected Graph

Author(s) -

Nasr Zeyada,

Anwar Saleh,

Majed Albaity,

Amr Kamel Amin

Publication year - 2022

Publication title -

journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.252

H-Index - 13

eISSN - 2314-4785

pISSN - 2314-4629

DOI - 10.1155/2022/8307871

Subject(s) - mathematics , degree matrix , algebraic connectivity , adjacency matrix , eigenvalues and eigenvectors , combinatorics , graph energy , graph , discrete mathematics , line graph , voltage graph , graph power , physics , quantum mechanics

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.

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