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On line graphs with maximum energy.
- Source :
-
Linear Algebra & its Applications . May2018, Vol. 545, p15-31. 17p. - Publication Year :
- 2018
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00243795
- Volume :
- 545
- Database :
- Academic Search Index
- Journal :
- Linear Algebra & its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 128278565
- Full Text :
- https://doi.org/10.1016/j.laa.2018.01.025