Name
Abstract | ||
|---|---|---|
Let G be a graph with vertex set V-G = {v(1),v(2), ..., v(n)} and edge set E-G, and let di be the degree of the vertex v(i). The ABC matrix of G has the value ,root(d(i) + d(j) - 2)/(d(i)d(j)) if v(i) v(j) is an element of E-G, and 0 otherwise, as its (i, j)-entry. Let gamma(1), gamma(2), ..., gamma(n) be the eigenvalues of the ABC matrix of G in a non-increasing order. Then the ABC Estrada index of G is defined as EEABC(G) = Sigma (n)(i=1) e(gamma i) and the ABC energy of G is defined as E-ABC(G) = Sigma(n)(i=1)vertical bar gamma(i)vertical bar. In this paper, some explicit bounds for the ABC Estrada index of graphs concerning the number of vertices, the number of edges, the maximum degree and the minimum degree, are established. Moreover, some bounds for the ABC Estrada index involving the ABC energy of graphs are also presented. All the corresponding extremal graphs are characterized respectively. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.disc.2021.112586 | DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
ABC matrix, ABC Estrada index, ABC energy | Journal | 344 |
Issue | ISSN | Citations |
11 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuchao Li | 1 | 183 | 35.15 |
| Lu Wang | 2 | 0 | 0.34 |
| huihui zhang | 3 | 30 | 7.61 |