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Spectra of graphs : theory and application
TLDR
The Spectrum and the Group of Automorphisms as discussed by the authors have been used extensively in Graph Spectra Techniques in Graph Theory and Combinatory Applications in Chemistry an Physics. But they have not yet been applied to Graph Spectral Biblgraphy.Abstract:
Introduction. Basic Concepts of the Spectrum of a Graph. Operations on Graphs and the Resulting Spectra. Relations Between Spectral and Structural Properties of Graphs. The Divisor of a Graph. The Spectrum and the Group of Automorphisms. Characterization of Graphs by Means of Spectra. Spectra Techniques in Graph Theory and Combinatories. Applications in Chemistry an Physics. Some Additional Results. Appendix. Tables of Graph Spectra Biblgraphy. Index of Symbols. Index of Names. Subject Index.read more
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Topics in algebraic combinatorics
TL;DR: In this article, the authors show that if φ(e) = uv (short for {u, v}), then e connects u and v or equivalently e is incident to u and V, then they call e a loop at v.
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Maximum energy trees with two maximum degree vertices
TL;DR: In this paper, it was shown that the maximum energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G in terms of the energy of the graph's energy function.
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Oriented hypergraphic matrix-tree type theorems and bidirected minors via Boolean order ideals
TL;DR: In this article, the determinant formula of a signed graphic Laplacian is reclaimed and shown to be determined by the maximal positive-circle-free elements, and spanning trees are equivalent to single-element order ideals.
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On the Generalized Distance Energy of Graphs
TL;DR: In this article, the generalized distance matrix of a simple connected graph G is defined as a convex combination of the convex combinations of T r (G ) + (1 − α ) D (G) for 0 ≤ α ≤ 1.
Minimal lel-equienergetic graphs
TL;DR: In this paper, Liu et al. considered LEL-equienergetic and almost-LEL-equifi-energetic graphs and found that they occur relatively rarely.