- Tytuł:
- Graphs with Clusters Perturbed by Regular Graphs—Aα-Spectrum and Applications
- Autorzy:
-
Cardoso, Domingos M.
Pastén, Germain
Rojo, Oscar - Powiązania:
- https://bibliotekanauki.pl/articles/31546556.pdf
- Data publikacji:
- 2020-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
cluster
convex combination of matrices
corona product of graphs
Aα-spectrum - Opis:
- Given a graph G, its adjacency matrix A(G) and its diagonal matrix of vertex degrees D(G), consider the matrix Aα(G) = αD(G) + (1 − α)A(G), where α ∈ [0, 1). The Aα -spectrum of G is the multiset of eigenvalues of Aα(G) and these eigenvalues are the α-eigenvalues of G. A cluster in G is a pair of vertex subsets (C, S), where C is a set of cardinality |C| ≥ 2 of pairwise co-neighbor vertices sharing the same set S of |S| neighbors. Assuming that G is connected and it has a cluster (C, S), G(H) is obtained from G and an r-regular graph H of order |C| by identifying its vertices with the vertices in C, eigenvalues of Aα(G) and Aα(G(H)) are deduced and if Aα(H) is positive semidefinite, then the i-th eigenvalue of Aα(G(H)) is greater than or equal to i-th eigenvalue of Aα(G). These results are extended to graphs with several pairwise disjoint clusters (C1, S1), . . ., (Ck, Sk). As an application, the effect on the energy, α-Estrada index and α-index of a graph G with clusters when the edges of regular graphs are added to G are analyzed. Finally, the Aα-spectrum of the corona product G ◦ H of a connected graph G and a regular graph H is determined.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2020, 40, 2; 451-466
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł