Eccentricity Laplacian energy of a graph
https://doi.org/10.17586/2220-8054-2024-15-5-567-575
Abstract
Let G be a simple, finite, undirected and connected graph. The eccentricity of a vertex v is the maximum distance from v to all other vertices of G. The eccentricity Laplacian matrix of G with n vertices is a square matrix of order n, whose elements are elij , where elij is −1 if the corresponding vertices are adjacent, elii is the eccentricity of vi for 1 ≤ i ≤ n, and elij is 0 otherwise. If ǫ1, ǫ2, . . . , ǫn are the eigenvalues of the eccentricity Laplacian matrix, then the eccentricity Laplacian energy of G is ELE(G) = Xn i=1 |ǫi − avec(G)| , where avec(G) is the average eccentricities of all the vertices of G. In this study, some properties of the eccentricity Laplacian energy are obtained and comparison between thge eccentricity Laplacian energy and the total π−electron energy is obtained.
About the Authors
A. Harshitha
Manipal Institute of Technology, Manipal Academy of Higher Education
India
India
A. Harshitha – Department of Mathematics, Manipal Institute of Technology
Manipal, 576104
S. Nayak
Manipal Institute of Technology, Manipal Academy of Higher Education
India
India
S. Nayak – Department of Mathematics, Manipal Institute of Technology
Manipal, 576104
S. D’Souza
Manipal Institute of Technology, Manipal Academy of Higher Education
India
India
S. D’Souza – Department of Mathematics, Manipal Institute of Technology
Manipal, 576104
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Review
For citations:
Harshitha A., Nayak S., D’Souza S. Eccentricity Laplacian energy of a graph. Nanosystems: Physics, Chemistry, Mathematics. 2024;15(5):567-575. https://doi.org/10.17586/2220-8054-2024-15-5-567-575
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