Degree subtraction eigenvalues and energy of graphs
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2024-03-19 12:01
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519.176 (1)
Analiză combinatorică. Teoria grafurilor (114)
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RAMANE, H. S., NANDEESH, K. C., GUDODAGI, G. A., ZHOU, B.. Degree subtraction eigenvalues and energy of graphs. In: Computer Science Journal of Moldova, 2018, nr. 2(77), pp. 146-162. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 2(77) / 2018 / ISSN 1561-4042 /ISSNe 2587-4330

Degree subtraction eigenvalues and energy of graphs

CZU: 519.176

Pag. 146-162

Ramane H. S.1, Nandeesh K. C.1, Gudodagi G. A.1, Zhou B.2
 
1 Department of Mathematics, Karnatak University,
2 South China Normal University
 
 
Disponibil în IBN: 12 septembrie 2018


Rezumat

The degree subtraction matrix DS(G) of a graph G is introduced, whose (j, k)-th entry is dG(vj) − dG(vk), where dG(vj) is the degree of a vertex vj in G. If G is a non-regular graph, then DS(G) has exactly two nonzero eigenvalues which are purely imaginary. Eigenvalues of the degree subtraction matrices of a graph and of its complement are the same. The degree subtraction energy of G is defined as the sum of absolute values of eigenvalues of DS(G) and we express it in terms of the first Zagreb index

Cuvinte-cheie
Degree of a vertex, degree subtraction matrix, eigenvalues, energy, first Zagreb index.