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Some New Bounds for α -Adjacency Energy of Graphs.
- Source :
-
Mathematics (2227-7390) . May2023, Vol. 11 Issue 9, p2173. 12p. - Publication Year :
- 2023
-
Abstract
- Let G be a graph with the adjacency matrix A (G) , and let D (G) be the diagonal matrix of the degrees of G. Nikiforov first defined the matrix A α (G) as A α (G) = α D (G) + (1 − α) A (G) , 0 ≤ α ≤ 1 , which shed new light on A (G) and Q (G) = D (G) + A (G) , and yielded some surprises. The α − adjacency energy E A α (G) of G is a new invariant that is calculated from the eigenvalues of A α (G) . In this work, by combining matrix theory and the graph structure properties, we provide some upper and lower bounds for E A α (G) in terms of graph parameters (the order n, the edge size m, etc.) and characterize the corresponding extremal graphs. In addition, we obtain some relations between E A α (G) and other energies such as the energy E (G) . Some results can be applied to appropriately estimate the α -adjacency energy using some given graph parameters rather than by performing some tedious calculations. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GRAPH theory
*EIGENVALUES
*STRUCTURAL analysis (Engineering)
*ENERGY consumption
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 11
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 163694433
- Full Text :
- https://doi.org/10.3390/math11092173