A note on heat kernel of graphs.
Heliyon
; 10(12): e32235, 2024 Jun 30.
Article
en En
| MEDLINE
| ID: mdl-39183868
ABSTRACT
Consider a simple undirected connected graph G, with D ( G ) and A ( G ) representing its degree and adjacency matrices, respectively. Furthermore, L ( G ) = D ( G ) - A ( G ) is the Laplacian matrix of G, and H t = exp â¡ ( - t L ( G ) ) is the heat kernel (HK) of G, with t > 0 denoting the time variable. For a vertex u ∈ V ( G ) , the uth element of the diagonal of the HK is defined as H t ( u , u ) = ( exp â¡ ( - t L ( G ) ) ) u u = ∑ k = 0 ∞ ( ( - t L ( G ) ) k ) u u k ! , and H E ( G ) = ∑ i = 1 n e - t λ i = ∑ u = 1 n H t ( u , u ) is the HK trace of G, where λ 1 , λ 2 , ⯠, λ n denote the eigenvalues of L ( G ) . This study provides new computational formulas for the HK diagonal entries of graphs using an almost equitable partition and the Schur complement technique. We also provide bounds for the HK trace of the graphs.
Texto completo:
1
Colección:
01-internacional
Base de datos:
MEDLINE
Idioma:
En
Revista:
Heliyon
Año:
2024
Tipo del documento:
Article
País de afiliación:
China
Pais de publicación:
Reino Unido