najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-3-315-324najo-57Research ArticleMATHEMATICSМАТЕМАТИКАEnergy and spectral radius of Zagreb matrix of graph with applicationsЭнергия и спектральный радиус Загребской матрицы графа с приложениямиhttps://orcid.org/0009-0004-0324-1835ШеттиШ. С.ShettySh. S.

Шашват С. Шетти

Манипальский технологический институт; кафедра математики

576104; Карнатака; Манипал

Shashwath S. Shetty

Manipal Institute of Technology; Department of Mathematics

576104; Karnataka; Manipal 

shashwathsshetty01334@gmail.comhttps://orcid.org/0000-0002-1526-5760БхатК А.BhatK. A.

К Арати Бхат

Манипальский технологический институт; кафедра математики

576104; Карнатака; Манипал

K. Arathi Bhat

Manipal Institute of Technology; Department of Mathematics

576104; Karnataka; Manipal 

arathi.bhat@manipal.eduМанипальская академия высшего образованияManipal Academy of Higher Education202401062025153315324Copyright © Shetty S.S., Bhat K.A., 20252025Шетти Ш.С., Бхат К.А.Shetty S.S., Bhat K.A.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/57

   The Z-matrix of a simple graph Γ is a square symmetric matrix, whose rows and columns correspond to the vertices of the graph and the ijth entry is equal to the sum of the degrees of ith and jth vertex, if the corresponding vertices are adjacent in Γ, and zero otherwise. The Zagreb eigenvalues of Γ are the eigenvalues of its Z-matrix and the Zagreb energy of Γ is the sum of absolute values of its Zagreb eigenvalues. We study the change in Zagreb energy of a graph when the edges of the graph are deleted or rotated. Suppose Γ is a graph obtained by identifying u ∈ V(Γ1) and v ∈ V(Γ2) or adding an edge between u and v, then it is important to study the relation between Zagreb energies of Γ1, Γ2 and Γ. The highlight of the paper is that, the acentric factor of n-alkanes appear to have a strong positive correlation (where the correlation coefficient is 0.9989) with energy of the Z-matrix. Also, the novel correlation of the density and refractive index of n-alkanes with spectral radius of the Z-matrix has been observed.

   Z-матрица простого графа Γ представляет собой квадратную симметричную матрицу, строки и столбцы которой соответствуют вершинам графа, а ij-й элемент равен сумме степеней i-й и j-й вершины, если соответствующие вершины смежны. в Γ и нулю в противном случае. Загребские собственные значения Γ являются собственными значениями его Z-матрицы, а загребская энергия Γ представляет собой сумму абсолютных значений его загребских собственных значений. Мы изучаем изменение загребской энергии графа при удалении или повороте ребер графа. Предположим, что Γ — граф, полученный отождествлением u ∈ V(Γ1) и v ∈ V(Γ2) или добавлением ребра между u и v, тогда важно изучить связь между загребскими энергиями Γ1, Γ2 и Γ. Изюминкой статьи является то, что ацентрический фактор н-алканов, по-видимому, имеет сильную положительную корреляцию (где коэффициент корреляции составляет 0,9989) с энергией Z-матрицы. Также наблюдалась новая корреляция плотности и показателя преломления n-алканов со спектральным радиусом Z-матрицы.

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