najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-5-567-575najo-87Research ArticleMATHEMATICSМАТЕМАТИКАEccentricity Laplacian energy of a graphЭксцентричность лапласиана энергии графаХаршитаА.HarshithaA.

A. Harshitha – Department of Mathematics, Manipal Institute of Technology

Manipal, 576104

aharshuarao@gmail.comНаякС.NayakS.

S. Nayak – Department of Mathematics, Manipal Institute of Technology

Manipal, 576104

swati.nayak@manipal.eduД’СоузаС.D’SouzaS.

S. D’Souza – Department of Mathematics, Manipal Institute of Technology

Manipal, 576104

sabitha.dsouza@manipal.eduManipal Institute of Technology, Manipal Academy of Higher EducationIndia202403062025155567575Copyright © Harshitha A., Nayak S., D’Souza S., 20252025Харшита А., Наяк С., Д’Соуза С.Harshitha A., Nayak S., D’Souza S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/87

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.

Пусть G – простой конечный неориентированный связный граф. Эксцентричность вершины v есть максимальное расстояние от v до всех остальных вершин графа G. Матрица эксцентричности лапласиана графа G с n вершинами – это квадратная матрица порядка n, элементы которой lij , где lij есть  -1, если соответствующие вершины соседние, lii  есть эксцентричность вершины vi  для I от 1 до n, lii  есть 0 в остальных случаях. Если  - собственные значения матрицы эксцентричности лапласиана энергии, то эксцентричность лапласиана энергии  G есть  где avec(G) средняя эксцентричность всех вершин G. В данном исследовании получены некоторые свойства эксцентричности лапласиана энергии  и проведено сравнение между эксцентричностью лапласиана энергии и полной энергией -электронов. 

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The authors declare that there are no conflicts of interest present.