
The notion of \(S\)-order of graphs has been studied, but few results are available. The characterizations of the first and the last graphs, in an \(S\)-order, of all trees, all unicyclic graphs with given girth, unicyclic graphs and bicyclic graphs are known, respectively. The paper determines the last and the second last quasi-tree, in an \(S\)-order, in the set, respectively.
Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), quasi-tree, Spectral moment, tree, spectral moment, Discrete Mathematics and Combinatorics, Quasi-tree, Geometry and Topology, Tree
Numerical Analysis, Eigenvalues, singular values, and eigenvectors, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), quasi-tree, Spectral moment, tree, spectral moment, Discrete Mathematics and Combinatorics, Quasi-tree, Geometry and Topology, Tree
| selected citations These citations are derived from selected sources. This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | 9 | |
| popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network. | Top 10% | |
| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
| impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network. | Average |
