Bounds on the ABC spectral radius of a tree
Let G be a simple connected graph with vertex set {1,2,...,n} and di denote the degree of vertex i in G. The ABC matrix of G, recently introduced by Estrada, is the square matrix whose ijth entry is √((di+dj-2)/didi); if i and j are adjacent, and zero; otherwise. The entries in ABC matrix represent...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2020-10-30.
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| LEADER | 02077 am a22002653u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_794_pdf_151 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Barik, Sasmita; School of Basic Sciences IIT Bhubaneswar, Bhubaneswar, 752050, India |e author |
| 100 | 1 | 0 | |e contributor |
| 700 | 1 | 0 | |a Rani, Sonu; School of Basic Sciences IIT Bhubaneswar, Bhubaneswar, 752050, India |e author |
| 245 | 0 | 0 | |a Bounds on the ABC spectral radius of a tree |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2020-10-30. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/794 | ||
| 520 | |a Let G be a simple connected graph with vertex set {1,2,...,n} and di denote the degree of vertex i in G. The ABC matrix of G, recently introduced by Estrada, is the square matrix whose ijth entry is √((di+dj-2)/didi); if i and j are adjacent, and zero; otherwise. The entries in ABC matrix represent the probability of visiting a nearest neighbor edge from one side or the other of a given edge in a graph. In this article, we provide bounds on ABC spectral radius of G in terms of the number of vertices in G. The trees with maximum and minimum ABC spectral radius are characterized. Also, in the class of trees on n vertices, we obtain the trees having first four values of ABC spectral radius and subsequently derive a better upper bound. | ||
| 540 | |a Copyright (c) 2020 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a tree, ABC matrix, ABC spectral radius, nonnegative matrix | ||
| 690 | |a 05C05, 05C35, 05C50, 92E10 | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 8, No 2 (2020): Electronic Journal of Graph Theory and Applications; 423 - 434 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/794/pdf_151 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/794/pdf_151 |z Get Fulltext |