On line graphs with maximum energy
| Autor: | María Robbiano, Eber Lenes, Exequiel Mallea-Zepeda, Z Jonnathan Rodríguez |
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| Rok vydání: | 2018 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Simple graph media_common.quotation_subject Vertex connectivity 0211 other engineering and technologies 021107 urban & regional planning 010103 numerical & computational mathematics 02 engineering and technology Inertia 01 natural sciences Upper and lower bounds Graph law.invention Vertex (geometry) Combinatorics law Line graph Discrete Mathematics and Combinatorics Geometry and Topology 0101 mathematics Eigenvalues and eigenvectors media_common Mathematics |
| Zdroj: | Linear Algebra and its Applications. 545:15-31 |
| ISSN: | 0024-3795 |
| Popis: | For an undirected simple graph G, the line graph L ( G ) is the graph whose vertex set is in one-to-one correspondence with the edge set of G where two vertices are adjacent if their corresponding edges in G have a common vertex. The energy E ( G ) is the sum of the absolute values of the eigenvalues of G. The vertex connectivity κ ( G ) is referred as the minimum number of vertices whose deletion disconnects G. The positive inertia ν + ( G ) corresponds to the number of positive eigenvalues of G. Finally, the matching number β ( G ) is the maximum number of independent edges of G. In this paper, we derive a sharp upper bound for the energy of the line graph of a graph G on n vertices having a vertex connectivity less than or equal to k. In addition, we obtain upper bounds on E ( G ) in terms of the edge connectivity, the inertia and the matching number of G. Moreover, a new family of hyperenergetic graphs is obtained. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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