Lower bounds for the algebraic connectivity of graphs with specified subgraphs
The second smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity and denoted by a(G). We prove thata(G)>π2/3(p(12g(n1, n2, ..., np)2 − π2)/4g(n1, n2, ..., np)4 + 4(q − p)(3g(np + 1, np + 2, ..., nq)2 − π2)/g(np + 1, np + 2, ..., nq)4),holds for every non-tr...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2021-10-16.
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| LEADER | 02390 am a22002533u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_995_pdf_177 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Stanic, Zoran; Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11 000 Belgrade, Serbia |e author |
| 100 | 1 | 0 | |e contributor |
| 245 | 0 | 0 | |a Lower bounds for the algebraic connectivity of graphs with specified subgraphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2021-10-16. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/995 | ||
| 520 | |a The second smallest eigenvalue of the Laplacian matrix of a graph G is called the algebraic connectivity and denoted by a(G). We prove thata(G)>π2/3(p(12g(n1, n2, ..., np)2 − π2)/4g(n1, n2, ..., np)4 + 4(q − p)(3g(np + 1, np + 2, ..., nq)2 − π2)/g(np + 1, np + 2, ..., nq)4),holds for every non-trivial graph G which contains edge-disjoint spanning subgraphs G1, G2, ..., Gq such that, for 1 ≤ i ≤ p, a(Gi)≥a(Pni), with ni ≥ 2, and, for p + 1 ≤ i ≤ q, a(Gi)≥a(Cni), where Pni and Cni denote the path and the cycle of the corresponding order, respectively, and g denotes the geometric mean of given arguments. Among certain consequences, we emphasize the following lower bounda(G)>π212(4q − 3p)n2 − (16q − 15p)π2/12n4,referring to G which has n (n ≥ 2) vertices and contains p Hamiltonian paths and q − p Hamiltonian cycles, such that all of them are edge-disjoint. We also discuss the quality of the obtained lower bounds. | ||
| 540 | |a Copyright (c) 2021 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a edge-disjoint subgraphs, Laplacian matrix, algebraic connectivity, geometric mean, Hamiltonian cycle | ||
| 690 | |a 05C50 | ||
| 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 9, No 2 (2021): Electronic Journal of Graph Theory and Applications; 257 - 263 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/995/pdf_177 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/995/pdf_177 |z Get Fulltext |